  Electron scattering in the topological surface state (TSS) of the
bulk-insulating topological insulator Bi$_{1.5}$Sb$_{0.5}$Te$_{1.7}$Se$_{1.3}$
was studied using quasiparticle interference observed by scanning tunneling
microscopy. It was found that not only the 180$^{\circ}$ backscattering but
also a wide range of backscattering angles of 100$^{\circ}$--180$^{\circ}$ is
effectively prohibited in the TSS. This conclusion was obtained by comparing
the observed scattering vectors with the diameters of the constant-energy
contours of the TSS, which were measured for both occupied and unoccupied
states using time- and angle-resolved photoemission spectroscopy. The
unexpectedly robust protection from backscattering in the TSS is a good news
for applications, but it poses a challenge to the theoretical understanding of
the transport in the TSS.
