# Watch HBO

Geometry Level 5

Consider a $$\Delta ABC$$ with $$\angle B=75^{\circ}$$. Let $$H$$ and $$O$$ be its $$\text{orthocenter and circumcenter respectively}$$. $$AD\bot BC$$ with $$D$$ on $$BC$$. Also $$AH\times HD=6(\sqrt{3}-1)$$ and circumradius of the $$\Delta ABC$$ is $$2\sqrt{3}~units$$.

$\large{\angle HBO=\arcsin \left(\frac{P}{Q}(\sqrt{R}-\sqrt{S}) \right)}$

where $$P,Q,R,S$$ are integers and $$P,Q$$ are co prime and $$R,S$$ are square free.

Find $$P+Q+R+S$$

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