Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle $varphi$ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D$^0$X. We find that polarimetry of the photon echo on the trion and D$^0$X is substantially different from the exciton: The echoes of the trion and D$^0$X are linearly polarized at the angle $2varphi$ with respect to the first pulse polarization and their amplitudes are weakly dependent on $varphi$. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as $cosvarphi$.
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