Fails to retain backer in Hollywood area (3,7)

I believe the answer is:

los angeles

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'hollywood area' is the definition.
'Los Angeles' can be an answer for 'area' (Los Angeles is an example). I am not certain of the 'hollywood' bit.

'fails to retain backer' is the wordplay.
'fails' becomes 'loses' (I've seen this before).
'to retain' means one lot of letters goes inside another.
'backer' becomes 'angel' (an angel is a financial backer).
'loses' going around 'angel' is 'LOS ANGELES'.

'in' acts as a link.

Can you help me to learn more?

(Other definitions for los angeles that I've seen before include "centre of population" , "LA, California" , "Big city" , "Californian city" , "Hollywood's city" .)

I've seen this clue in The Independent.

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