Prove that `cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 theta`.

Explanation

To prove that \( \cos^3 \theta \sin 3\theta + \sin^3 \theta \cos 3\theta = \frac{3}{4} \sin 4\theta \), we will start by using the known identities for \( \sin 3\theta \) and \( \cos 3\theta \).

### Step 1: Use the identities for \( \sin 3\theta \) and \( \cos 3\theta \)

The formulas for \( \sin 3\theta \) and \( \cos 3\theta \) are:
\[ \sin 3\theta = 3\sin \theta - 4\sin^3 \theta \]
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