This is a basic physics and math problem
and your very initial idea for solving it is wrong!
Light waves travel linearly. When they hit a reflective surface, they change direction according to entry-angle is equal to exit-angle, a shown above. The green-marked path hits the center. Unless the mirror is a curve or we actually use a laser, the outer bounds of the ray will be diverging - the Fisheye effect, shown with the red and yellow paths.
Now, let'S for simplicity assume we have a laser. by twisting the mirror by -2° on the red path and +2° on the yellow we get the same picture of divergent paths.
To keep the rays parallel we may not adjust the angle, but only the distance of our initial mirror: to hit more on the far side of our rotational mirror and get a stream that is parallel to the one when we hit the center, we need to move further away (red), to hit closer we need to move it shorter (yellow).
Instead of varying the distance, the mirror could also move on a curved path to create the shifted parallel rays needed: