Anthem is taken lyrically partly the wrong way (10)

I believe the answer is:

mistakenly

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'wrong way' is the definition.
'mistakenly' can be an answer for 'wrong' (thesaurus). I'm not sure about the 'way' bit.

'anthem is taken lyrically partly' is the wordplay.
'partly' indicates a hidden word (part of the clue is used).
'MISTAKENLY' is hidden in the letters of 'anthem is taken lyrically'.

'the' is the link.

Can you help me to learn more?

(Another definition for mistakenly that I've seen is " in error".)

I've seen this clue in The Telegraph.

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