In various situations for performing complex transformations first we need to align an arbitrary line with the standard axis. To align the standard axis with an arbitrary line it is important to know the angle of rotations.

As show in the figure above the angle θ₂ is the angle for rotation about x axis so as to align z axis with the projection of A₁A₂ on YZ plane. Thereafter with the same position of z axis rotation of θ₂ is taken about Y axis which aligns the Z axis with the arbitrary line. The angles can be calculated as below.