I took a course relating to this sort of thing a few months ago. The topic was "Dynamics of Machines". You can break this problem down and get to the solution, using techniques that have been developed.
Here's a course a found online that will certainly have the technique in it somewhere, I...
At optimal angle to horizontal, for your latitude and time of year, there is a single angle if you do not have the lazy susan. The sun should move through a plane at perpendicular to the plane of the panel. The sun should pass through a point normal to the panel at high noon. With the panel...