How to determine the compressive force in the spars of a strutted wing?
It's very easy. Consider that the point at which the strut is attached does not accelerate, i.e., the forces in all directions exactly even out.

The force in the spanwise direction exerted by the strut is

$$F_{strut}^{spanwise}=\cos\theta\cdot F_{strut}$$

This force must be balanced by the wing in compression, so the above expression is also valid for the amount of compression on the wing.

This assumes the strut only transfers longitudinal forces, while in reality it may have some bending stiffness. Also, I'm not sure where you got your equation for the tension in the strut, but it's not necessarily true (there's a lot more structural members exerting a vertical force on the wing, so the force- and moment balance is not as simple).