Kindly show all the steps and working.

3. Consider a bead constrained to move along a wire that makes an angle with respect to the upward vertical. The wire rotates about the vertical as shown in Fig 2 with an angular velocity . As. always, the force of gravity acts vertically downwards. Compute the Lagrangian for the system using an appropriate set of generalised coordinates. Figure 2: Bead on a rotating wire. Given that the constraints of the motion are given by: x=rsinsinty=rsincostz=rcos Show that L=21m(r2+2r2sin2)mgrcos