Boundary Values & Fourier Series · Medium problem

Solve $u_t = 2u_{xx}$ on $0 < x < \pi$ with $u(0,t) = u(\pi,t) = 0$ and $u(x,0) = 3\sin x - \sin 3x$. Find $u\!\left(\dfrac\pi2, \dfrac{\ln 2}{2}\right)$.