Let $c = \frac{2\pi}{11}.$ What is the value of \[ \frac{\sin 3c \cdot \sin 6c \cdot \sin 9c \cdot \sin 12c \cdot \sin 15c}{\sin c \cdot \sin 2c \cdot \sin 3c \cdot \sin 4c \cdot \sin 5c}? \]

Let's think step by step and output the final answer within \boxed{}.
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