Pully/spring equilibrium (statics)

[kirab]

Diagram attached.

The spring is unstretched when theta = 0. Determine the theta for equilibrium.

I'm not quite sure how to get started here. My prof said that we cannot assume that the tension in the 400 N force cable at A is equal to the tension at the spring close to fixed support C (because it isn't a frictionless pulley).

If we could make this assumption, I'd have the answer! But we can't. Any suggestions? Thanks.

 

[PhanthomJay]

The system is in equilibrium at a certain value of theta. If you sum moments about point O and set them equal to zero, you get your first equation with theta and the spring force as unknowns. Your second equation comes from Hooke's law for the spring. How much does the spring stretch at the equilibrium position?