Question

if cot2θ = tan4θ , where 2θ and 4θ are acute angles, find the value of sin 3θ

Answer 1

$\cot2 \theta = \tan 4\theta \\ \tan(90 - 2 \theta) = \tan 4\theta \\ 90 - 2 \theta = 4\theta \\ 6\theta = 90 \\ 3\theta = 45 \\ \sin3\theta = \sin(45) = \frac{1}{ \sqrt{2} }$