What's this function?

Geometry Level 4

r=0nnCrsin(rx)cos((nr)x)=f(n)sin(nx)\large \displaystyle \sum^{n}_{r=0} {^{n}C_{r} \sin(rx) \cos((n-r)x)=f(n)\sin(nx)}

Let f(n)f(n) denote a function such that the equation above is an identity.

Find the value of f(15)f(15).

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