Boundary Values & Fourier Series · Medium problem

A string obeys $u_{tt} = 4u_{xx}$ on $0 < x < \pi$ with fixed ends. It starts flat, $u(x,0) = 0$, with uniform velocity $u_t(x,0) = 1$. Writing $u = \sum_{n\ge1} B_n\sin nx\sin 2nt$, find $B_1$.