Essentially I have a 4 bar linkage with all 4 link lengths known, and 2 angle measurements known. I am trying to solve the other 2 angle measurements based on these 4 link lengths and 2 angle measurements. If I can figure out an equation for one of the unknown angles based on the known values, the other one should be trivial. But whenever I try to figure out the math the equations "blow up" into more and more terms and I don't know how to develop the problem to get things to cancel out.

I have spent a few months on this and I keep getting stuck, and would appreciate any help. I'm a 36 year old Engineer and am banging my head on the table on this simple problem, so any help would be greatly appreciated. Note that this is a personal project and is not based on homework in any way.