Crossword Genius

Private and seaman in double act, ditching uniform and tux (6,6)


I believe the answer is:

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'tux' is the definition.

'private and seaman in double act ditching uniform' is the wordplay.
I cannot really see how this works, but
'private' could be 'inner' (I've seen this before) and 'inner' is found in the answer.
This explanation may well be incorrect...

'and' is the link.

Can you help me to learn more?

(Other definitions for dinner jacket that I've seen before include "Man's formal garment", "Tuxedo", "Formal male evening attire".)

I've seen this clue in The Telegraph.