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Detectives work out how to cross Swords (8)

Ross

I believe the answer is:

disagree

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'to cross swords' is the definition.
I can't judge whether this definition defines the answer.

'detectives work out' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'work out' becomes 'agree' (I am not sure about this - if you are sure you should believe this answer much more).
'dis'+'agree'='DISAGREE'

'how' acts as a link.

Can you help me to learn more?

(Other definitions for disagree that I've seen before include "Row" , "Express a contrary view" , "Differ, dissent" , "dispute" , "Have conflicting opinions" .)

I've seen this clue in the Irish Times (Crosaire) and The Irish Times.
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