  We studied magneto-optical response of a canonical topological insulator
Bi$_2$Se$_3$ with the goal of addressing a controversial issue of
electron-phonon coupling. Magnetic-field induced modifications of reflectance
are very pronounced in the infrared part of the spectrum, indicating strong
electron-phonon coupling. This coupling causes an asymmetric line-shape of the
60 cm$^{-1}$ phonon mode, and is analyzed within the Fano formalism. The
analysis reveals that the Fano asymmetry parameter (q) changes sign when the
cyclotron resonance is degenerate with the phonon mode. To the best of our
knowledge this is the first example of magnetic field driven q-reversal.
