ELMO 2003 Problem 1

Let $ABCDEF$ be a convex equilateral hexagon with sides of length $1$ . Let $R_1$ be the area of the region contained within both $ACE$ and $BDF$ , and let $R_2$ be the area of the region within the hexagon outside both triangles. Prove that: $$\min \{ [ACE], [BDF] \} + R_2 - R_1 \le \frac{3\sqrt{3}}{4}.$$