Generalized Euler Angle Parameterization for U(N) with Applications to   SU(N) Coset Volume Measures
  In a previous paper (math-ph/0205016) an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CP(N) as well as other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived. 
Todd Tilma, E.C.G. Sudarshan