If block d weighs 300 lb and block b weighs 275 lb determine the required weight of block c and the angle theta for equilibrium?

Set up a free body diagram. 

and by reason, Tcd = Tbd 

Tbd y = 275 - 300*sinθ 
Tcd y = Tc - 300*sin30 

Tbd x = 300*cosθ 
Tcdx = 300 * cos30 

Tbd^2 = (275 - 300*sinθ)^2 + (300*cosθ)^2 
Tcd^2 = (300*sin30)^2 + (300 * cos30)^2 

(275 - 300*sinθ)^2 + (300*cosθ)^2 = (300*sin30)^2 + (300 * cos30)^2 
etc.