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Stock-Based Compensation - Details of Nonvested Restricted Stock Units Activity (Detail) (USD $)
In Thousands, except Share data, unless otherwise specified
1 Months Ended 12 Months Ended
Feb. 28, 2014
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of Restricted Stock Units, Granted, Nonvested 380,064us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod 380,064us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod    
Restricted Stock Units [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of Restricted Units Outstanding, Beginning Balance, Nonvested   60,686us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Number of Restricted Stock Units, Granted, Nonvested   181,500us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Number of Restricted Stock Units, Vested   (46,144)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Number of Restricted Stock Units , Accrued Dividend Equivalents, Nonvested   1,796ctb_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedAccruedDividendEquivalents
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Number of Restricted Units Outstanding, Ending Balance, Nonvested   197,838us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
60,686us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Weighted Average Grant-Date Fair Value, Nonvested, Beginning Balance   22.61us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Weighted average grant-date fair value of restricted shares granted   27.53us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 25.72us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 15.54us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Weighted Average Grant-Date Fair Value, Vested   25.69us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Total fair value of shares vested   1,185us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 1,122us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 1,495us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Weighted Average Grant-Date Fair Value, Accrued dividend equivalents   31.40ctb_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsAccruedDividendEquivalentsWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Weighted Average Grant-Date Fair Value, Nonvested, Ending Balance   26.48us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 22.61us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember