computing the Haar measure for O(n) and U(n) groups My question is about how to compute the Haar measure for O(n) and U(n) groups. 
For example, for the conventional parametrization of SO(3) with 3 angels, the Haar measure is
$ dO= cos(\theta_{13})*d\theta_{12}*d\theta_{13}*d\theta_{23}$ .
How one derives this formula? I want to compute the Haar measure for both O(n) and U(n) for general n. 
I am a student of physics and I am not quite familiar with Haar measure. 

You might like these lecture notes. In particular, the second page discusses such calculations.
