Analytical Solution of an symbolic set of equations

I tried solving a set of symbolic equations but it keeps running and yields no result. The set of equations are:

a^2 + b^2 = A, a c \exp{(\iota \theta)} + bd\exp{(\iota \phi)} = B, c^2\exp{(2\iota \theta)} + d^2\exp{(2\iota \phi)} = C, c^2 + d^2 = D

Since, the number of variables exceeds the number of equations I was hoping to find the solutions (symbolic) in terms of $ a$ .