A smooth circular hoop of radius \(R = 0.40 \text{ m}\) is oriented vertically and rotates at a constant angular speed \(\omega\) about its vertical central diameter. A small bead is threaded onto the hoop and slides along it with negligible friction. When the hoop rotates, the bead maintains a constant position on the hoop at an angle \(\theta = 60^\circ\) measured from the lowest point of the hoop. What is the angular speed \(\omega\) of the hoop?