An analysis of a rotating rod

Consider a uniform rod of mass MM and length L,L, free to rotate around a frictionless axis passing through its center and going into the page. Initially, the rod is stationary in the horizontal position, as shown in the diagram below.

Now, a small bullet of mass mm moving with velocity vv hits the rod at its extreme end and sticks to it. The system rotates vertically through some angle θ\theta before it momentarily comes to rest. If this angle can be expressed (in degrees) as θ=α+arcsin(βmv2(M+γm)gL),\theta = \alpha + \arcsin \left(\frac {\beta mv^2}{( M+\gamma m)gL}\right), where gg denotes the gravitational acceleration and α\alpha, β\beta, and γ\gamma are positive integer constants with α\alpha in degrees, then find the value of α+β+γ\alpha + \beta + \gamma .

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