What is \frac{\sin \theta-2 \sin^3 \theta}{2 \cos^3 \theta-\cos \theta} equal to?

Explanation

Factor out \sin \theta and \cos \theta: \frac{\sin \theta(1 - 2\sin^2 \theta)}{\cos \theta(2\cos^2 \theta - 1)}. Using double angle formulas, both bracketed terms are equal to \cos 2\theta, canceling out to leave \frac{\sin \theta}{\cos \theta} = \tan \theta.

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