\(a_1,a_2,a_3\) are in arithmetic progression in which common difference is \(2\) and the first term is \(2\). If
\[
\cos a_1+\cos a_2+\cos a_3
=
\frac{\sin\alpha}{\sin\beta}\cos\gamma,
\]
then \(\alpha+\beta=\)
Show Hint
For three cosine terms in arithmetic progression,
\[
\boxed{\cos(A-d)+\cos A+\cos(A+d)
=\cos A\,(1+2\cos d).}
\]
Then use
\[
\boxed{\sin3x=\sin x\,(1+2\cos2x)}
\]
to simplify further.