Modern gears have lead and profile modifications. In other words, the tooth surface modeled as discussed above is modified a special way to allow the gears to operate correctly. Get a special 3d gear modeling software - it is easy to find.
I would just do it in CAD like SolidWorks on solid models of the gears. Two options. 1. Place a normal in the middle of the tooth surface and measure the required angles. 2. Assemble the gears with a small interference and subtract - you will get a face on the tooth surface - immediate tooth...