Prove the identity ( 3theta - 3theta)/(1 - 2 2theta) = theta + theta. Identify any errors in the solution.

Your initial steps are correct:

1. You correctly expanded $\cos 3\theta$ and $\sin 3\theta$ using the triple angle formulas: $\cos 3\theta = 4\cos^3\theta - 3\cos\theta$ $\sin 3\theta = 3\sin\theta - 4\sin^3\theta$ And the denominator using the double angle formula: $1 - 2