Find the deflection $u(x, t)$ of a vibrating string of length $\pi$, extending from $x = 0$ to $x = \pi$, and $c^2 = 4$ starting with velocity zero and deflection.
$F(x) = \sin^3x$
Hint: $\sin(3x) = \sin(x + 2x)$, $\sin(\alpha + \beta) = \sin\alpha\cos\beta + \sin\beta\cos\alpha$