# Algebraic condition from a non linear equation

I have got a system of equations which look like this:

$\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega z)}{1+be^{-\phi_{0}}e^{-\phi_{1}\cos(\Omega z)}\sin^{2}(2\theta_{1}\sin\Omega z)}=0$

and similarly for the other one. I don't want to solve this equations in $z$, but just treat them as algebraic equations to extract some conditions on $\theta_1, \phi_1$. This means, I want to check under what conditions on the constants, this equations have a solution.

By hand, what I would do is to write down the series expansion of all the $\sin(\sin\Omega z)$-like terms, and then integrate over 0 to $\pi$ to make some terms vanish. But since here the expressions are horrible, I was wondering if Mathematica could help me getting the conditions or at least some insight in this kind of problems.

This is a much more general class of equations or at least common calculations Physics people are usually interested in, and could be useful for a lot of different scopes apart from my toy problem.

-
Why not to make the procedure you have in mind (i.e. the expansion of functions like sin(sinΩz)) within Mathematica? Have a look at Menu/Help/Series. –  Alexei Boulbitch Dec 16 '13 at 16:34