Sines and pies

Geometry Level 5

sinπ14sin3π14sin5π14sin7π14sin9π14sin11π14sin13π14 =2n\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 nn.

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