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Prove that: sin((pi)/5)sin((2pi)/5)sin((...

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

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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 can follow these steps: ### Step 1: Use the properties of sine We know that: \[ \sin\left(\frac{3\pi}{5}\right) = \sin\left(\pi - \frac{2\pi}{5}\right) = \sin\left(\frac{2\pi}{5}\right) \] and ...
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