# A Polygon Flower

Geometry Level 5

Regular Polygons are arranged around a unit equilateral triangle as shown in the figure above.

If the hatched area can be written as $\frac{1}{d} \frac{\sqrt{a}-\sqrt{b}}{\sqrt{3d(\sqrt{c}+c)}+\sqrt{c}-1}$ for square-free integers $$a, b, c$$ and $$d$$. Find $$a+b+c+d$$.

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