A trig identity

Geometry Level 4

Given that cos2θ=1+54 \cos2\theta = \dfrac{1+\sqrt5}4 , if tan2(3θ)tan2(θ) \tan^2 (3\theta) \tan^2(\theta) is equal to mn \dfrac mn, where mm and nn are coprime positive integers, find m+nm+n.


Adapted from Purdue Problem of the week.
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