  Wolpert's cosine formula on Teichm\"uller space gives the Weil-Petersson
Poisson bracket $\{l_\alpha, l_\beta\}$ for geodesic length functions
$l_\alpha,l_\beta$ of closed curves $\alpha,\beta$ as the sum of the cosines of
the angle of intersection of the associated geodesics. This was recently
generalized to Hitchin representations by Labourie. In this paper, we give a
short proof of this generalization using Goldman's formula for the Poisson
bracket on representation varieties of surface groups into reductive Lie
groups.
