Note 6 - Inventories - Changes in Provision for Obsolete Inventories (Details) - USD ($) $ in Thousands	9 Months Ended	12 Months Ended
Mar. 31, 2024	Jun. 30, 2023
Beginning	$ 648	$ 674
Additions charged to expense	35	61
Usage – disposition	(19)	(40)
Currency translation effect	5	(47)
Ending	$ 669	$ 648

Represents currency translation effect.

No definition available.

Name:	trt_CurrencyTranslationEffect
Namespace Prefix:	trt_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The increase (decrease) during the reporting period in the book value of finished goods inventory and work in process inventory.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

+ Details

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

- Definition

Reflects the amount charged against earnings comprised of the costs to announce and effect a recall of defective merchandise.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_InventoryRecallExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of valuation reserve for inventory.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 330
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.BB)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480581/330-10-S99-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(6))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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