A small bead of mass \(m\) slides along the frictionless outer surface of a stationary vertical circular hoop of radius \(R = 5.0\text{ m}\). The bead is initially at the highest point of the hoop and is given an initial horizontal speed \(v_0 = 3.5\text{ m/s}\). Let \(\theta\) be the angle between the upward vertical and the position vector of the bead measured from the center of the hoop. At what angle \(\theta\) does the bead lose contact with the hoop?