A small bead of mass \(m\) is threaded onto a thin, vertical wire hoop of radius \(R\). The hoop rotates about its vertical diameter with a constant angular velocity \(\omega\), as shown. The bead moves with the hoop and remains at a fixed position at an angle \(\theta\) relative to the vertical axis passing through the bottom of the hoop. Assuming there is no friction between the bead and the wire, which of the following is a correct expression for \(\cos\theta\)?