  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\%.
