Hi,
I was trying to derive the same equations of motion,
Why have you considered the RHS of second equation = constant ?

I got:-  m(L^2) * [  (sin theta)^2 * phi_dot_dot  +  sin(2*theta) * theta_dot * phi_dot  ]  =    0
as the second eq of Motion.

After this, how to solve?

regards,
tito