Organised duet with CD? Take it away! (6)

I believe the answer is:

deduct

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'take it away' is the definition.
I can't judge whether this definition defines the answer.

'organised duet with cd?' is the wordplay.
'organised' indicates anagramming the letters.
'with' says to put letters next to each other.
'duet' after 'cd' is 'cdduet'.
'cdduet' anagrammed gives 'DEDUCT'.

Can you help me to learn more?

(Other definitions for deduct that I've seen before include "Make a subtraction" , "Subtract, take away" , "Remove" , "Knock off" , "Withhold" .)

I've seen this clue in The Irish Times.

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