Using itegration by parts I could probably kick this thing off...
Not really sure how to do,
probably needs some trig identities to tidy it up.
It can be done using complex variables...
First note that
Parameterize the unit circle in the comples plane with
So the integral becomes
expanding with the binomial theorem we get
each finite sume is its own larent series so the residues are coeffients on the terms so we get