Just a reminder that the system can be reduced to two equations if you
eliminate A and B from the system. (e.g. solve expressions 0 and 2 for A
and B and then solve the remaining two equations for Phi and theta). Using
sympy's nsolve gives:
>>> nsolve([e1,e3],[Phi,theta],[0.1,.5])
matrix(
[['-0.942845232974915'],
['0.68171791938912']])
>>> nsolve([e1,e3],[Phi,theta],[0.2,.5])
matrix(
[['0.0453589103507513'],
['1.02936055239276']])