MathNet 2011 Question 43

Points $D$, $E$, $F$ lie on circle $O$ such that the line tangent to $O$ at $D$ intersects ray $\overrightarrow{E F}$ at $P$. Given that $P D = 4$, $P F = 2$, and $\angle F P D = 60^{\circ}$, determine the area of circle $O$.