Exercise 11.4.4

In the inner product space $C[-\pi,\pi]$, consider the orthogonal set of functions from Example 11.26: $\left\{1,\sin x,\cos x,\sin 2x,\cos 2x,\sin 3x,\cos 3x,\ldots\right\}$. Let $f(x)=x^{2}$, where $x\in[-\pi,\pi]$. Find the Fourier series of $f$.