Boredom to an extent rotten nuisance (5)

I believe the answer is:

ennui

'boredom' is the definition.
('ennui' can be a synonym of 'boredom')

'to an extent rotten nuisance' is the wordplay.
'to an extent' says the answer is hidden in the clue.
'ENNUI' is hidden within 'rotten nuisance'.

(Other definitions for ennui that I've seen before include "Result of boredom" , "having nothing to do" , "Boredom, listlessness" , "Lower interest rate" , "World-weariness" .)

I've seen this clue in The Times and The Sun.

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