In a cult, going mad. Quite mad (7)

I believe the answer is:

lunatic

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'quite mad' is the definition.
'lunatic' can be an answer for 'mad' (I've seen this before). I'm unsure of the 'quite' bit.

'in a cult going mad' is the wordplay.
'going mad' indicates anagramming the letters.
'in'+'a'+'cult'='inacult'
'inacult' with letters rearranged gives 'LUNATIC'.

Can you help me to learn more?

(Other definitions for lunatic that I've seen before include "Maniac" , "Bats" , "Crazy" , "Harebrained" , "Mad" .)

I've seen this clue in The Telegraph.

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