I don't know if this is the best way to go about it, but perhaps you can express the function as a convolution of a half wave with a train of delta functions (or something like that).
|sin(t)| = sin(t) on [0, pi], and |sin(t)| = -sin(t) on [pi, 2pi] or on [-pi, 0]
Thanks - I thought of this as well, but this would mean I have to integrate on each interval, and I get sum(n=0, n=inf) ((1+exp(pi*s)/exp(n*pi*s)*(s^2+1)). Is there a way to simplify this? I'm supposed to be using Laplace transforms to solve a differential equation with |sint| as the inhomogeneous part.