Prove that: `sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)`

Explanation

To prove that \( \sin\left(\frac{\pi}{5}\right) \sin\left(\frac{2\pi}{5}\right) \sin\left(\frac{3\pi}{5}\right) \sin\left(\frac{4\pi}{5}\right) = \frac{5}{16} \), we will follow these steps:

### Step 1: Rewrite the Sine Functions
We know that:
- \( \sin\left(\frac{3\pi}{5}\right) = \sin\left(\pi - \frac{2\pi}{5}\right) = \sin\left(\frac{2\pi}{5}\right) \)
- \( \sin\left(\frac{4\pi}{5}\right) = \sin\left(\pi - \frac{\pi}{5}\right) = \sin\left(\frac{\pi}{5}\right) \)

Thus, we can rewrite the expression as:
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