A ring of negligible mass remains in static equilibrium under the influence of three coplanar forces, as shown in the accompanying diagram. Two forces, each with a magnitude of \(10\,\text{N}\), act on the ring at an angle \(\theta\) above the horizontal—one directed to the right and the other to the left. A third force, \(F\), acts vertically downward. Determine the magnitude of force \(F\).