  Twisted graphene multi-layers have been recently demonstrated to share
several correlation-driven behaviours with twisted bilayer graphene. In
general, the van Hove singularities (VHSs) can be used as a proxy of the
tendency for correlated behaviours. In this paper, we adopt an atomistic method
by combining tight-binding method with the semi-classical molecular dynamics to
investigate the electronic structures of twisted trilayer graphene (TTG) with
two independent twist angles. The two independent twist angles can lead to the
interference of the moir\'e patterns forming a variety of
commensurate/incommensurate complex supermoir\'e patterns. In particular, the
lattice relaxation, twist angle and angle disorder effects on the VHS are
discussed. We find that the lattice relaxation significantly influence the
position and magnitude of the VHSs. In the supermoir\'e TTG, the moir\'e
interference provides constructive or destructive effects depending on the
relative twist angle. By modulating the two independent twist angles, novel
superstructures, for instance, the Kagome-like lattice, could constructed via
the moir\'e pattern. Moreover, we demonstrate that a slight change in twist
angles (angle disorder) provides a significant suppression of the peak of the
VHSs. Apart from the moir\'e length, the evolution of the VHSs and the LDOS
mapping in real space could be used to identify the twist angles in the
complicated TTG. In practice, our work could provide a guide for exploring the
flat band behaviours in the supermoir\'e TTG experimentally.
