  Stacking three monolayers of graphene with a twist generally produces two
moir\'e patterns. A moir\'e of moir\'e structure then emerges at larger
distance where the three layers periodically realign. We devise here an
effective low-energy theory to describe the spectrum at distances larger than
the moir\'e lengthscale. In each valley of the underlying graphene, the theory
comprises one Dirac cone at the ${\bf \Gamma}_M$ point of the moir\'e Brillouin
zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The
velocities and small gaps exhibit a spatial dependence in the
moir\'e-of-moir\'e unit cell, entailing a non-abelian connection potential
which ensures gauge invariance. The resulting model is numerically solved and a
fully connected spectrum is obtained, which is protected by the combination of
time-reversal and twofold-rotation symmetries.
