Prove that: `sin(pi/14)sin((3pi)/14)sin((5pi)/14)sin((7pi)/14)sin((9pi)/14)sin((11pi)/14)sin((13pi)/14)=1/(64)`

Explanation

To prove that

\[ \sin\left(\frac{\pi}{14}\right) \sin\left(\frac{3\pi}{14}\right) \sin\left(\frac{5\pi}{14}\right) \sin\left(\frac{7\pi}{14}\right) \sin\left(\frac{9\pi}{14}\right) \sin\left(\frac{11\pi}{14}\right) \sin\left(\frac{13\pi}{14}\right) = \frac{1}{64}, \]

we can use the properties of sine and cosine functions along with some trigonometric identities.

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