Given three angles $\theta_1,\theta_2,\theta_3\in[0,2\pi)$, and a non-zero constant $K\in\mathbb{R}$, is it possible to solve the following equations analytically? \begin{equation} \begin{cases} \sin(\theta_1-\theta_2)+\sin(\theta_1-\theta_3)=K\sin(2\theta_1)\\ \sin(\theta_2-\theta_1)+\sin(\theta_2-\theta_3)=K\sin(2\theta_2)\\ \sin(\theta_3-\theta_1)+\sin(\theta_3-\theta_2)=K\sin(2\theta_3)\\ \end{cases} \end{equation}
Note that when $K=0$ it can be easily solved.
