@dharr Thanks so much, this helped a lot! I got closer by using different constraints, however not close enough. By including another equation I got an solution extremely close to the exact one. I guess you were right that several combinations would work with only the four original equations. Thanks again.

Regarding seting x=Pi/2: When doing this with an unknown solution, x will very likely not be equal to Pi/2 and therefore unfortunately I cannot do that. That would have my life a lot easier though.