The aching part due to wagging? (4)

I believe the answer is:

chin

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'due to wagging?' is the definition.
I can't judge whether this defines the answer.

'the aching part' is the wordplay.
'part' says the answer is hidden in the clue.
'CHIN' is hidden within 'aching'.

Can you help me to learn more?

(Other definitions for chin that I've seen before include "Punch to the face" , "Feature of face" , "Keep it up and be optimistic" , "Protruding part of lower jaw" , "part of mug" .)

I've seen this clue in the Evening Standard.

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