Boundary Values & Fourier Series · Hard problem

A rod $0 \le x \le \pi$ obeys $u_t = u_{xx}$, with $u(0, t) = 0$ and an insulated right end $u_x(\pi, t) = 0$. Initially $u(x, 0) = \sin\dfrac{x}{2} + \sin\dfrac{3x}{2}$. Find $u(\pi, 4\ln 2)$.