Prove that: `sin^3A+sin^3((2pi)/3+A)+sin^3((4pi)/3+A)=-3/4sin3Adot`

Explanation

To prove that \( \sin^3 A + \sin^3 \left( \frac{2\pi}{3} + A \right) + \sin^3 \left( \frac{4\pi}{3} + A \right) = -\frac{3}{4} \sin 3A \), we will follow these steps:

### Step 1: Write the left-hand side
We start with the left-hand side of the equation:
\[ LHS = \sin^3 A + \sin^3 \left( \frac{2\pi}{3} + A \right) + \sin^3 \left( \frac{4\pi}{3} + A \right) \]

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