Sines and pies

Geometry Level 4

\[\large \sin\dfrac{\pi}{14}\sin\dfrac{3{\pi}}{14}\sin\dfrac{5{\pi}}{14}\sin\dfrac{7{\pi}}{14}\sin\dfrac{9{\pi}}{14}\sin\dfrac{11{\pi}}{14}\sin\dfrac{13{\pi}}{14}\ = 2^n\]

Find \(n\).

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