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