We get the following equations---
cosθ1 + cosθ2 = 1/6 ..............(1)
sinθ1 + sin(θ1-θ2) = 4/5 ..............(2)
cosθ3 - cos(θ3+θ4) = 5/6 ...............(3)
sinθ3 + sin(θ3 + θ4) = 4/5 ..............(4)
After solving these equations we get the following solutions----
θ1=145°
θ2=131.8°
θ3=100°
θ4=109°