Make mad, awfully enraged or otherwise angered (7)

I believe the answer is:

derange

I'm a little stuck... Click here to teach me more about this clue!

'make mad' is the definition.
(I've seen this in another clue)

'otherwise angered' is the wordplay.
'otherwise' indicates an anagram.
'angered' anagrammed gives 'DERANGE'.

'awfully enraged or' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for derange that I've seen before include "Make mad" , "Remove from order" , "Unhinge" , "Upset" , "Craze" .)

I've seen this clue in The Guardian.

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