I am given a system
$$ \dot{\theta_1} = C - \sin{\theta_1} + D\sin{(\theta_2-\theta_1)}, $$ $$ \dot{\theta_2} = C + \sin{\theta_2} + D\sin{(\theta_1-\theta_2)}, $$
$$ C,D \geq 0 $$
and asked to find the fixed points.
Right now I am rewriting it in terms of
$$\phi_1 = \theta_1 - \theta_2$$ and $$\phi_2 = \theta_1 + \theta_2$$ and using "brute force" to solve it. However, I am not very satisfied with the lengthy and messy calculation, so does anyone have any thoughts on how to solve this problem in some neat way?