Minotaur in Crete injuring heads with teeth (10)

I believe the answer is:

incidental

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'minotaur in crete injuring heads with teeth' is the definition.
I can't tell whether this defines the answer.

'in crete injuring heads with teeth' is the wordplay.
'heads' suggests taking the first letters.
'with teeth' becomes 'dental' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The initial letters of 'crete injuring' is 'ci'.
'in'+'ci'+'dental'='INCIDENTAL'

Can you help me to learn more?

(Other definitions for incidental that I've seen before include "fortuitous" , "By the way" , "form of music" , "Not an essential" .)

I've seen this clue in the Sydney Morning Herald.

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