Laplace Transforms · Superchallenge problem

Let $f = \sin * \sin * \sin$ be the triple convolution, $f(t) = \big((\sin * \sin) * \sin\big)(t)$ with $(g * h)(t) = \displaystyle\int_0^t g(\tau)h(t - \tau)\,d\tau$. Using the Laplace transform, find $f(\pi)$.