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°