(beginner) calculating orientation change with eulers

[astull]

Is the non-unique solution due to the selection of 90 degrees as the pitch angle? Ultimately, I need a unique solution. Is it reasonable to assume that this might be addressed by calculating the difference for a 3rd vector? I don't know the math so I'm only assuming the following modified script would retrieve the necessary values from the matrix to calculate a 3rd vector:

#Extract forward/up vector from euler1
m.setRot( vizmat.EulerToAxisAngle(euler1) )
d = m.get()
forward1 = d[8:11]
up1 = d[4:7]
side1 = d[12:3]

#Extract forward/up vector from euler2
m.setRot( vizmat.EulerToAxisAngle(euler2) )
d = m.get()
forward2 = d[8:11]
up2 = d[4:7]
side2 = d[12:3]

Am I wondering in the dark?

Alternatively, wouldn't a unique solution also result if I calculated the displacement from the facing direction AND the angle of rotation about that axis (the facing direction)?