I wrote a clarification to your previous question which I think should resolve that issue. It looks like you have determined (or can determine) a, c and phi and wish to solve for b and theta. The first equation in your question is just the imaginary part of
a*exp(i*x) + b*exp(i*x + i*theta) = c*exp(i*x + i*phi)
Factoring out the exp(i*x) leaves
a + b*exp(i*theta) = c*exp(i*phi)
so the sum of two phasors is a third one. [ note that multiplying this equation by its complex counjugate gives the second equation in the question ]. Solving this gives
b = abs(c*exp(i*phi) - a)
theta = angle(c*exp(i*phi) - a)
Just like acos, angle has a convention that deals with 2pi ambiguity, which is -pi < angle <=pi. This means that for the case that you mentioned, angle will produce -120 degrees, not 240. That's how it is, but if you want only positive angles, then (for degrees) it would be mod(angle,360).