  We investigate Fabry-Perot interference in an ultraclean carbon nanotube
resonator. The conductance shows a clear superstructure superimposed onto
conventional Fabry-Perot oscillations. A sliding average over the fast
oscillations reveals a characteristic slow modulation of the conductance as a
function of the gate voltage. We identify the origin of this secondary
interference in intervalley and intravalley backscattering processes which
involve wave vectors of different magnitude, reflecting the trigonal warping of
the Dirac cones. As a consequence, the analysis of the secondary interference
pattern allows us to estimate the chiral angle of the carbon nanotube.
