Cook knighted in a movie (3,4,3,1)

I believe the answer is:

the king and i

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'movie' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'cook knighted in a' is the wordplay.
'cook' is an anagram indicator.
'knighted'+'in'+'a'='knightedina'
'knightedina' anagrammed gives 'THE KING AND I'.

Can you help me to learn more?

(Other definitions for the king and i that I've seen before include "Bangkok-setting musical" , "Film/musical set in Siam" , "Musical set in old Thailand" , "Show" , "Rodgers and Hammerstein musical" .)

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