Cutie pi!

Geometry Level 5

sin(π14)sin(3π14)sin(5π14)sin(7π14)sin(9π14)sin(11π14)sin(13π14) \large \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)

If the expression above can be simplified to the form pq \frac pq for coprime positive integers, find p+qp+q.

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