What's this "Taylor series about x of zero= pi" business? The last I heard was that

is not equal to 0. I will assume you mean an expansion about 0.

According to Taylor's theorem, a function f(x) expanded about the point x = a is:

So we need the derivatives of

evaluated at x = 0.

etc.

In fact what we can do is this:

so we can write the Taylor series of x about x = 0 and the Taylor series of sin(x) about x = 0 and add them:

(I'll leave it to you to do enough terms to verify that the sin(x) series is correct.)

-Dan