How can I derive (even approximately) the distribution of the random variable $$\Delta=\cos\phi_1-\cos\phi_2$$ if I know the following two facts about the random variables $\phi_1$ and $\phi_2$?
1) $\phi_1-\phi_2\approx \mathcal{N}(0,\tau)$ (i.e. the difference is normally distributed)
2) $\phi_1$ and $\phi_2$ are uniform in $[-\pi,\pi]$
