The Unit Circle and Circular Functions · Superchallenge problem

Let $A=(1,0)$, and for $k=0,1,2,\dots,11$ let $P_k$ be the terminal point on the unit circle of the angle $\dfrac{k\pi}{6}$. Find $\displaystyle\sum_{k=0}^{11}AP_k^{\,2}$, the sum of the squared distances from $A$ to the twelve points.