Note 21 - Leases (Details Textual) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Dec. 31, 2025	Dec. 31, 2024	Dec. 31, 2025
Lessor Asset under Operating Lease, Term (Year)			20 years
Depreciation, Lessor Asset under Operating Lease	$ 17	$ 16
Minimum [Member]
Lessor, Operating Lease, Term of Contract (Month)	12 months		12 months
Lessee, Operating Lease, Remaining Lease Term (Year)	1 year		1 year
Maximum [Member]
Lessor, Operating Lease, Term of Contract (Month)	48 years		48 years
Lessee, Operating Lease, Remaining Lease Term (Year)	5 years		5 years

Represents term for lessor asset under operating lease.

No definition available.

Name:	trt_LessorAssetUnderOperatingLeaseTerm
Namespace Prefix:	trt_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Remaining lease term of operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-7A

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseRemainingLeaseTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Term of lessor's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479773/842-30-50-3

+ Details

Name:	us-gaap_LessorOperatingLeaseTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of depreciation expense for lessor's underlying asset for which right to use has been conveyed to lessee under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479773/842-30-50-13

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482099/360-10-50-1

+ Details

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

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: