HMMT 2003 G8

Let $A B C$ be an equilateral triangle of side length 2 . Let $\omega$ be its circumcircle, and let $\omega_{A}, \omega_{B}, \omega_{C}$ be circles congruent to $\omega$ centered at each of its vertices. Let $R$ be the set of all points in the plane contained in exactly two of these four circles. What is the area of $R$ ?