I have this equation:
$$\lambda \sin(2 \alpha)+ \sin(2 \alpha \lambda)=0$$
where "$\alpha$" is a known parameter and my desire is to calculate eigenvalues, "$\lambda$". I've tried some newton-raphson and muller codes in Matlab, but it didn't work since I know eigenvalues for some alphas. for example, for $\alpha=\pi/3$, first eigenvalue becomes $0.5122$ and it becomes complex for second one and after. I hope I've explained it clearly.