The specific features of the electronic and spin structures of a triple topological insulator Bi₂Te_2.4Se_0.6, which is characterized by high-efficiency thermoelectric properties, have been studied with the use of angular- and spin-resolved photoelectron spectroscopy and compared with theoretical calculations in the framework of the density functional theory. It has been shown that the Fermi level for Bi₂Te_2.4Se_0.6 falls outside the band gap and traverses the topological surface state (the Dirac cone). Theoretical calculations of the electronic structure of the surface have demonstrated that the character of distribution of Se atoms on the Te–Se sublattice practically does not influence the dispersion of the surface topological electronic state. The spin structure of this state is characterized by helical spin polarization. Analysis of the Bi₂Te_2.4Se_0.6 surface by scanning tunnel microscopy has revealed atomic smoothness of the surface of a sample cleaved in an ultrahigh vacuum, with a lattice constant of ~4.23 Å. Stability of the Dirac cone of the Bi₂Te_2.4Se_0.6 compound to deposition of a Pt monolayer on the surface is shown.