Hi! I've stumbled upon an equation of the form:

e^{-i k x} + R e^{i (k x + \theta)} = i k \xi \left( e^{-i k x} - R e^{i (k x + \theta)}\right)

I wish to solve the equation for complex k. Every other constants are known and real.  0 \leq R \leq 1,~\xi > 0. Does there exist a complete analytic solution for k, or perhaps a solution in some approximate limit? At least I know that for R = 0,~k = -\frac{i}{\xi}.