Let \triangle A B C be an isosceles triangle with A B=A C=\sqrt{7} and B C=1. Let G be the centroid of \triangle A B C. Given j \in\{0,1,2\}, let T_{j} denote the triangle obtained by rotating \triangle A B C about G by 2 \pi j / 3 radians. Let \mathcal{P} denote the intersection of the interiors of triangles T_{0}, T_{1}, T_{2}. If K denotes the area of \mathcal{P}, then K^{2}=\frac{a}{b} for relatively prime positive integers a, b. Find a+b.