Boundary Values & Fourier Series · Hard problem

A string on $0 \le x \le \pi$ with fixed ends obeys $u_{tt} = u_{xx}$ and is released from rest with $u(x, 0) = \sin x + 2\sin 2x$. Its energy $E = \dfrac12\displaystyle\int_0^\pi\left(u_t^2 + u_x^2\right)dx$ is constant in time. Find $E$.