Cutie pi!

Geometry Level 5

\[ \large \sin\left( \frac \pi{14} \right) \sin\left( \frac {3\pi}{14} \right) \sin\left( \frac {5\pi}{14} \right) \sin\left( \frac {7\pi}{14} \right) \sin\left( \frac {9\pi}{14} \right) \sin\left( \frac {11\pi}{14} \right) \sin\left( \frac {13\pi}{14} \right) \]

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

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