Solving underdetermined nonlinear system of 2 equation with 3 unknowns.

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I've gotten into a problem I haven't really worked with before in my numerics classes.

I have an underdetermined nonlinear system of equations with 3 real-valued parameters, precisely those parameters are angles $\in$ $[0,\pi/2]$. The system is defined as:

\begin{align} \begin{cases} A=\cos(\alpha)e^{i\phi}\\ B=\sin(\alpha)e^{i\chi} \end{cases} \end{align} where $A$ and $B$ are two known complex-valued parameters.

Newtons method, Boydens method etc. all include the inverse of the jacobian, but if the system is underdetermined this is not defined as far as I understand Is there any straightforward way or trick to solve this kind of problems?