Solve system of equations

[Gribouillis]

Unfortunately, I don't have much time to help you now but I think you reduced too fast the complex equations to real numbers. Go back to the complex equations and try to interprete them in geometrical terms. It seems to me that with some work you could express Cs in terms of L and Rs, then design an optimisation form of the problem. When I have the time to do so, I may answer in more details but I'm afraid it won't be before a week because I'm going to be on a journey for a few days.