Two identical particles, each with mass \(m\) and positive charge \(q\), are injected into a uniform magnetic field \(\vec{B}\). Particle 1 enters with speed \(v_1\) at an angle of \(30^\circ\) relative to the direction of \(\vec{B}\), and Particle 2 enters with speed \(v_2\) at an angle of \(60^\circ\) relative to \(\vec{B}\). Both particles follow helical paths that have the same radius \(R\). What is the ratio of the pitch of Particle 2's path to the pitch of Particle 1's path, \(\dfrac{p_2}{p_1}\)?