use a maclaurin series to obtain the maclaurin series for the given function f(x)= (sinx)^2 hint use (sinx)^2 = 1/2(1-cos2x)
Basically this amounts to finding the maclaurin series for cos(u) since then you can just put in a 2x for u (then multiply by your 1/2 scalar and subtract from 1/2). Note this trick works because the radius of convergence for this series turns out to be infinite, more care should in general be used.
so finally you see:
Think you can take her from here?