Answer
See below.
Work Step by Step
$LHS=\frac{sin(2\theta)+sin(4\theta)}{cos(2\theta)+cos(4\theta)}=\frac{2sin(\frac{2\theta+4\theta}{2})cos(\frac{2\theta-4\theta}{2})}{2cos(\frac{2\theta+4\theta}{2})cos(\frac{2\theta-4\theta}{2})}=tan(3\theta)=RHS$
