We have analyzed the depolarized light scattering (DLS) spectrum of a viscoelastic polymer liquid in which the dielectric constant anisotropy (DCA) is modulated by both chain segmental reorientation and local shear strain fluctuations. Using linear response theory, we have first shown that in the absence of chain segmental reorientation, the DLS spectrum is the imaginary part of the dynamic shear compliance spectrum of the polymer liquid. When both segmental reorientation and shear strain fluctuations are present, the DLS spectrum is complex. In the case that the reorientation rate is fast, we have shown that the DLS spectrum becomes the sum of reorientational and dynamic shear compliance spectra. As part of the DCA is relaxed by molecular reorientation, the DLS spectrum becomes the dynamic shear compliance spectrum associated with the strain fluctuations. Thus, the DLS spectrum of the polymer liquid measured at long times (or low frequency) corresponds to a dynamic shear compliance spectrum. The present work generalizes the results previously presented in which the molecular reorientation is assumed to be slow. The result of the present theoretical analysis thus shows that it is possible to determine the dynamic shear compliance spectra of polymer liquids by using DLS.