Crossword Genius

Destroy nasty coat whatever the consequences (2,3,4)

Ross

I believe the answer is:

at any cost

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'whatever the consequences' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'destroy nasty coat' is the wordplay.
'destroy' indicates anagramming the letters (I've seen this in other clues).
'nasty'+'coat'='nastycoat'
'nastycoat' anagrammed gives 'AT ANY COST'.

Can you help me to learn more?

(Other definitions for at any cost that I've seen before include "Regardless of the price to pay" , "whatever the damage" .)

I've seen this clue in The Independent.
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