Answer
$0.0114^\circ$
Work Step by Step
First, we need to stick a flat mirror on the side that faces the laser beam gun, as shown below.
So when the cylinder rotates an angle of $\theta$, the angle between the incident and reflected beam is then $2\theta$.
And since the angle $2\theta$ is too small, we can use the approximation of $\tan(2\theta)\approx 2\theta$.
Thus,
$$2\theta=\dfrac{d}{L}$$
Hence,
$$\theta=\dfrac{d}{2L}=\dfrac{2\times 10^{-2}}{2(5)}=\bf 2\times 10^{-4}\;\rm rad$$
$$\theta=\color{red}{\bf 0.0114}^\circ$$
