(a) Plot the first four Brillouin zones for a 2-dimensional hexagonal lattice in both the extended and reduced zone schemes. (b) Inscribe a free electron Fermi sphere such that the Fermi surface just reaches the center of the second zone in the reduced zone representation. Shade the regions of electron occupation in the four reduced zones determined in part (a). (c) Qualitatively modify your drawing of the fourth zone to include effects of Bragg scattering at the Brillouin zone boundaries.