Boundary Values & Fourier Series · Challenge problem

A damped string obeys $u_{tt} + 2u_t = u_{xx}$ on $0 < x < \pi$ with fixed ends, $u(x, 0) = \sin 2x$ and $u_t(x, 0) = 0$. Find $u\!\left(\dfrac\pi4, \dfrac{\pi}{\sqrt3}\right)$.