The Unit Circle and Circular Functions · Superchallenge problem

Let $A = (1, 0)$, and for $k = 1, 2, \ldots, 11$ let $P_k$ be the terminal point on the unit circle of the angle $\dfrac{k\pi}{6}$. Find the product of the eleven distances $AP_1\cdot AP_2\cdots AP_{11}$.