Note 4 - Trade Accounts Receivable and Allowance for Expected Credit Losses - Allowance for Doubtful Accounts (Details) - USD ($) $ in Thousands	9 Months Ended	12 Months Ended
Mar. 31, 2024	Jun. 30, 2023
Beginning	$ 217	$ 243
Additions charged to expense	12	9
Recovered	(17)	(20)
Currency translation effect	2	(15)
Ending	$ 214	$ 217

Represents effect on accounts receivable for currency translation.

No definition available.

Name:	trt_CurrencyTranslationEffectOnAccountsReceivable
Namespace Prefix:	trt_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of allowance for credit loss on accounts receivable.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479344/326-20-45-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-4

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

+ Details

Name:	us-gaap_AllowanceForDoubtfulAccountsReceivable
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of increase (decrease) in allowance for credit loss on accounts receivable.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

+ Details

Name:	us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of increase in allowance for credit loss on accounts receivable, from recovery.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

+ Details

Name:	us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration