# $$\sin (2\alpha+\beta)$$

Geometry Level 2

Line segment $$AB$$ is a diameter of circle $$\Gamma.$$ Take a point $$C$$ on $$\Gamma$$ such that $$\overline{AC}=5$$ and $$\overline{BC}=1.$$ If $$\angle CAB=\alpha$$ and $$\angle CBA=\beta,$$ what is the value of $$\sin (2\alpha+\beta)?$$

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