Macroscopic rotors are interesting model systems to test quantum theory and for quantum sensing. A promising approach for bringing these systems to the quantum regime is to combine sensitive detection with feedback cooling to reduce the thermal occupation of the mechanics. Here, we implement a backward-scattering scheme to efficiently detect all three libration modes of an optically levitated nanoparticle. We demonstrate parametric feedback cooling of all three libration degrees of freedom to below 16 mK, with one of the modes reaching the temperature of 1.3 mK, corresponding to a mean phonon number of 84. Finally, we characterize the backward-scattering scheme by determining its measurement efficiency to be 0.5%.