Unravelling big oil promo uncovered embarrassing entanglement (9)

I believe the answer is:

imbroglio

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'embarrassing entanglement' is the definition.
'imbroglio' can be an answer for 'entanglement' (I've seen this in another clue). I'm unsure of the 'embarrassing' bit.

'unravelling big oil promo uncovered' is the wordplay.
'unravelling' indicates anagramming the letters.
'uncovered' indicates the central letters.
The centre of 'promo' is 'rom'.
'big'+'oil'+'rom'='bigoilrom'
'bigoilrom' is an anagram of 'IMBROGLIO'.

Can you help me to learn more?

(Other definitions for imbroglio that I've seen before include "Oilrig mob (anag.)" , "Jumble" , "Confused and tangled situation" , "Dilemma" , "Confused situation results" .)

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