Solving Trigonometric Equation. 
Solve for $\theta$ $[0°<\theta<180°]$
  $$\sin2\theta + \sin4\theta=\cos\theta + \cos3\theta.$$

My solution is here:
$$\sin2\theta + \sin4\theta=\cos\theta + \cos3\theta.$$
After using the transformation formula, I got
$$\sin3\theta\cos\theta=\cos3\theta\cos\theta.$$
I could not proceed from here.

Using Prosthaphaeresis Formulas as suggested,
$$ \sin 2\theta+\sin 4\theta = \cos \theta+\cos 3\theta \\
  2\sin 3\theta \cos \theta = 2\cos 2\theta \cos \theta \\
  \cos \theta \, (\sin 3\theta-\cos 2\theta) = 0 $$
If $\cos \theta=0,\theta=(2n+1)90^\circ$ where $n$ is any integer
We need $0<(2n+1)90^\circ<180^\circ\implies-1<n<1\implies n=0$
Else $\cos 2\theta=\sin 3\theta=\cos(90^\circ-3\theta)$
$2\theta=360^\circ m\pm(90^\circ-3\theta)$
$+\implies\theta=72^\circ m+18^\circ$ and we need $0<72^\circ m+18^\circ<180^\circ\implies m=?$
$-\implies\theta=-360^\circ m+90^\circ$
Can you take it from here?
