# BID for the angle

Geometry Level 5

Given in the figure, a $$\Delta ABC$$ with sides $$AB=3\sqrt{2}-\sqrt{6}$$, $$AC=3\sqrt{2}+\sqrt{6}$$ and $$BC=6$$ units. $$AD$$ is the angle bisector of $$\angle BAC$$, with $$D$$ on $$BC$$. $$I$$ is the in-center of $$\Delta ABC$$.

$\large{\angle BID=\cot^{-1} \left(\sqrt{P}+\sqrt{Q}-\sqrt{R}-S \right)}$

where $$P,Q,R,S$$ are integers with $$P,Q,R$$ being square free. Find the value of $$P+Q+R+S$$.

Clarification: $$\cot^{-1} (x)=\text{arccot} (x)$$.

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