A small spherical ball undergoes an elastic collision with a rough horizontal surface. Before the collision, it is moving at an angle of \(\theta\) with the horizontal. Assume that friction \(f=\mu N\) during the contact period, where \(N\) is the normal reaction and \(\mu\) is the coefficient of friction.

Find the value of \(\theta\) (in degrees) to the nearest integer such that the horizontal range of the ball after hitting the surface is maximized, given \(\mu=\frac{\sqrt{3}}{2}\).

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