Rephrasing an old problem, I'm looking forward to finding the roots in $x$ of the following trigonometric function: $$\sin\left({\frac{\gamma(x\sqrt{C^2-\gamma^2x^2}-(x+B)\sqrt{C^2-\gamma^2(B-x)^2}+2(T-C)B)}{C^2}}\right)-\frac{\gamma(x\sqrt{C^2-\gamma^2(B-x)^2}+(B-x)\sqrt{C^2-\gamma^2x^2}}{C^2}=0$$
Where $B,C,\gamma,T$ are constant parameters. I already know that the function has a real root depending on the values of the parameters but I have no clue how to start solving it. If anyone could help me I would truly appreciate.