Cog $A$ is at position: $Ax$, $Ay$, rotation: $Ar$ and number of teeth: $At$
Cog $B$ is at position: $Bx$, $By$ and number of teeth $Bt$. What is Cog $B$'s rotation such that teeth between Cog $A$ and Cog $B$ line up. There will be the same number of answers as there are teeth, but a 'base angle' is desired.