Cardan Angle Calculation

Hi,

I am searching for a method how to calculate 5-axis CNC machine 4th and 5th axis rotations when a direction vector (xyz) is given.

I have following two axis, so called cardan angles, where the 5th axis is rotated by 50 degrees.
Is there any code I could look at how to compute the two rotations?

For orthogonal axes I use this formula, but this does not work for such a rotated case:
    double a = Math.Atan2(n0.X, n0.Y);
    double b = Math.Atan2(Math.Sqrt(n0.X * n0.X + n0.Y * n0.Y), n0.Z);