Let $c=\frac{2\pi }{17}$. What is the value of

$\frac{\sin 2c\cdot \sin 4c\cdot \sin 6c\cdot \sin 8c\cdot \sin 10c\cdot \sin 12c\cdot \sin 14c\cdot \sin 16c}{\sin c\cdot \sin 2c\cdot \sin 3c\cdot \sin 4c\cdot \sin 5c\cdot \sin 6c\cdot \sin 7c\cdot \sin 8c}?$