  We consider a configuration of three stacked graphene monolayers with equal
consecutive twist angles $\theta$. Remarkably, in the chiral limit when
interlayer coupling terms between $\textrm{AA}$ sites of the moir\'{e} pattern
are neglected we find four perfectly flat bands (for each valley) at a sequence
of magic angles which are exactly equal to the twisted bilayer graphene (TBG)
magic angles divided by $\sqrt{2}$. Therefore, the first magic angle for
equal-twist trilayer graphene (eTTG) in the chiral limit is $\theta_{*} \approx
1.05^{\circ}/\sqrt{2} \approx 0.74^{\circ}$. We prove this relation
analytically and show that the Bloch states of the eTTG's flat bands are
non-linearly related to those of TBG's. Additionally, we show that at the magic
angles, the upper and lower bands must touch the four exactly flat bands at the
Dirac point of the middle graphene layer. Finally, we explore the eTTG's
spectrum away from the chiral limit through numerical analysis.
