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Cambridge eccentric losing male budgerigar, for example (4,4)

Ross

I believe the answer is:

cage bird

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'cambridge eccentric losing' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'male budgerigar for example' is the wordplay.
'male' becomes 'cage' (I can't explain this - if you can you should give a lot more credence to this answer).
'budgerigar for example' becomes 'bird' (budgerigar is a kind of bird).
'cage'+'bird'='CAGE-BIRD'

Can you help me to learn more?

(Other definitions for cage bird that I've seen before include "One tweeting often shut up" , "Canary, say" .)

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