for this function :
M(X,Y,Z) =
| cosYcosZ -cosYsinZ sinY |
| sinXsinYcosZ+cosXsinZ -sinXsinYsinZ+cosXcosZ -sinXcosY |
| -cosXsinYcosZ+sinXsinZ cosXsinYsinZ+sinXcosZ cosXcosY |
you can have 2 couples ( X1,Y1,Z1) and ( X2,Y2,Z2 ) which gives you EXACTLY
the same matrix, more generaly M(X,Y,Z) is surjective but not injective so
it is not bijective !!!
it is why the ONLY way to invert is to do : y=Arcsin(m13) etc etc which
gives you ONE of the 2 possible couples ...
the only way to get rid of this and to get bijectivity is to allow Y to be
between -pi/2 and pi/2 for example ... and in this case only ONE couple
will match and you function will be inversible ...