Become tired of cigarette (3)

I believe the answer is:

fag

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'cigarette' is the definition.
(I know that cigarette can be written as fag)

I cannot understand how the remainder of the clue works.

(Other definitions for fag that I've seen before include "smoke" , "Boring task" , "Ciggie" , "Tiring task; cigarette" , "Tedious chore" .)

I've seen this clue in the Evening Standard.

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