The value of `sinpi/(14)sin(3pi)/(14)sin(5pi)/(14)sin(7pi)/(14)sin(9pi)/(14)sin(11pi)/(14)sin(13pi)/(14)` is equal to___________

Explanation

To solve the given expression \(\sin\left(\frac{\pi}{14}\right) \sin\left(\frac{3\pi}{14}\right) \sin\left(\frac{5\pi}{14}\right) \sin\left(\frac{7\pi}{14}\right) \sin\left(\frac{9\pi}{14}\right) \sin\left(\frac{11\pi}{14}\right) \sin\left(\frac{13\pi}{14}\right)\), follow these steps:

### Step 1: Use Symmetry Properties of Sine Function
Recall that \(\sin(\pi - \theta) = \sin(\theta)\). This property helps us simplify the terms:
- \(\sin\left(\frac{9\pi}{14}\right) = \sin\left(\pi - \frac{9\pi}{14}\right) = \sin\left(\frac{5\pi}{14}\right)\)
- \(\sin\left(\frac{11\pi}{14}\right) = \sin\left(\pi - \frac{11\pi}{14}\right) = \sin\left(\frac{3\pi}{14}\right)\)
- \(\sin\left(\frac{13\pi}{14}\right) = \sin\left(\pi - \frac{13\pi}{14}\right) = \sin\left(\frac{\pi}{14}\right)\)

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