In future electron-positron colliders, such as FC-ee and CEPC, it is planned to accurately measure the beam energy by resonance depolarization. In this paper, we propose an alternative approach based on the rapid resonant rotation of the spins into the horizontal plane of the ring and their subsequent free rotation around the equilibrium vertical direction. The frequency of free coherent spin precession is proposed to be measured by the beats of the number of scattering events of electrons interacting with circularly polarized laser light. Fourier analysis of the number of electrons dropped out of the ring aperture to determine the frequency of free precession. In this paper, spin dynamics is simulated at all stages of the process, taking into account synchrotron oscillations and energy diffusion, and statistical estimates of the accuracy of determining the frequency of spin precession for beam parameters in FCC-ee are made.