The reflectance and transmittance of light by plane-parallel crystal plates were found in the exciton-transition spectral region upon oblique incidence of light with polarization in which two transverse and one longitudinal normal exciton-polariton wave are excited. The reflection spectra calculated for a model crystal with the parameters of the CdSe crystal are analyzed for different thicknesses of the plates, angles of incidence, and damping constants. It is shown that accounting for additional exciton-polariton waves and multiple reflections of light inside the plate results in the possibility of an abrupt change in the phase (by more than 2π) in the vicinity of the exciton transition.