Boundary Values & Fourier Series · Medium problem

A string $0 \le x \le \pi$ with fixed ends obeys $u_{tt} = u_{xx}$. It starts flat, $u(x, 0) = 0$, with initial velocity $u_t(x, 0) = \sin x + 3\sin 2x$. Find $u\!\left(\dfrac\pi4, \dfrac\pi4\right)$.