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

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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