Question 62
There exist several solutions to the equation
$$
1 + \frac{\sin x}{\sin 4x} = \frac{\sin 3x}{\sin 2x}
$$
where $x$ is expressed in degrees and $0^{\circ} \lt x \lt 180^{\circ}$. Find the sum of all such solutions.
$$
1 + \frac{\sin x}{\sin 4x} = \frac{\sin 3x}{\sin 2x}
$$
where $x$ is expressed in degrees and $0^{\circ} \lt x \lt 180^{\circ}$. Find the sum of all such solutions.