Answer
See below.
Work Step by Step
$LHS=\frac{cos2\theta-cos4\theta}{cos2\theta+cos4\theta}-tan\theta tan(3\theta)
=\frac{-2sin\frac{2\theta+4\theta}{2}sin\frac{2\theta-4\theta}{2}}{2cos\frac{2\theta+4\theta}{2}cos\frac{2\theta-4\theta}{2}}-tan\theta tan(3\theta)
=tan(3\theta)tan\theta -tan\theta tan(3\theta)=0
=RHS$
