MathNet 2021 — Part 10 Question 1

Question 1

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

-1
$-\frac{\sqrt{11}}5$
$\frac{\sqrt{11}}5$
$\frac{10}{11}$
1