Boundary Values & Fourier Series · Challenge problem

A string $0 \le x \le \pi$ with fixed ends obeys $u_{tt} = u_{xx}$. It is plucked into the triangle $u(x, 0) = \dfrac{2x}{\pi}$ for $0 \le x \le \dfrac\pi2$, $u(x, 0) = \dfrac{2(\pi - x)}{\pi}$ for $\dfrac\pi2 \le x \le \pi$, and released from rest. Find $u\!\left(\dfrac\pi2, \dfrac{3\pi}{4}\right)$.