A mechanic uses a wrench to loosen a bolt. In Scenario 1, the mechanic applies a force of magnitude \(F\) at a distance \(R\) from the center of the bolt such that the force is perpendicular to the wrench handle. In Scenario 2, the mechanic applies the same force of magnitude \(F\) at a distance \(2R\) from the center of the bolt, but the angle between the force vector and the handle is now \(30^{\circ}\). What is the ratio \(\dfrac{\tau_2}{\tau_1}\) of the torque produced in Scenario 2 to the torque produced in Scenario 1?