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Note 17 - Contract Balances (Details Textual) - USD ($) $ in Thousands | Mar. 31, 2022 | Jun. 30, 2021
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Revenue, Remaining Performance Obligation, Amount | $ 636 | $ 924
Minimum [Member] |  |
Percentage of Contract Consideration | 70.00% |
Maximum [Member] |  |
Percentage of Contract Consideration | 90.00% |
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period (Year) | 2 years |

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- Definition Represents percentage of contract consideration. + References No definition available. + Details
Name: | trt_PercentageOfContractConsideration
Namespace Prefix: | trt_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | instant

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- Definition Amount of transaction price allocated to performance obligation that has not been recognized as revenue. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 606 -SubTopic 10 -Section 50 -Paragraph 13 -Subparagraph (a) -URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130556-203045 + Details
Name: | us-gaap_RevenueRemainingPerformanceObligation
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Period in which remaining performance obligation is expected to be recognized as revenue, 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 -Publisher FASB -Name Accounting Standards Codification -Topic 606 -SubTopic 10 -Section 50 -Paragraph 13 -Subparagraph (b)(1) -URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130556-203045 + Details
Name: | us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1
Namespace Prefix: | us-gaap_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | instant

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

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