A regular hexagon with center at the origin in the complex plane has opposite pairs
of sides one unit apart. One pair of sides is parallel to the imaginary axis.
Let R be the region outside the hexagon, and let S=\left\{\frac{1}{z} \mid z \in R\right\}.
Then the area of S has the form a \pi+\sqrt{b}, where a and b are positive integers.
Find a+b.