Measurements of magnetoresistance anisotropy in a quasi-two-dimensional conductor (BEDT-TTF)2TlHg(SCN)4 have been performed. Giant angular magnetoresistance oscillations have been found upon rotating the magnetic field in different planes perpendicular to the highly conducting ac-plane. The phenomenon is proposed to be associated with specifics of th electron motion along the open FS sheets under the magnetic field. The analysis of the oscillations reveals some qualitative differences between a calculated high temperature position of the open Fermi surface sheets and that found at low temperatures