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Capital supplement, is the music group getting across? (5,5)

Ross

I believe the answer is:

addis ababa

'capital' is the definition.
(capital of Ethiopia)

'supplement is the music group getting across?' is the wordplay.
'supplement' becomes 'add' (I've seen this before).
'the music' becomes 'a'.
'group' becomes 'ABBA'.
'getting across?' indicates putting letters inside.
'a' placed inside 'abba' is 'ababa'.
'add'+'is'+'ababa'='ADDIS ABABA'

(Other definitions for addis ababa that I've seen before include "African capital" , "Capital of Ethiopia" , "Unaccompanied" , "Ethiopia's capital" , "African city" .)

I've seen this clue in The Hindu.
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