  The ability to identify and characterize spontaneous symmetry breaking is
central to our understanding of 2D materials with strong correlation, such as
the moir\'e flat bands in magic-angle twisted graphene bilayer and trilayer. In
this work, we utilize angle-resolved measurements of transport nonreciprocity
to investigate spontaneous symmetry breaking in twisted trilayer graphene. By
analyzing the angular dependence of nonreciprocity in both longitudinal and
transverse channels, we are able to identify the symmetry axis associated with
the underlying electronic order. We report that a hysteretic rotation in the
mirror axis can be induced by thermal cycles and a large current bias, which
offers unambiguous evidence for the spontaneous breaking of rotational
symmetry. Moreover, the onset of nonreciprocity with decreasing temperature
coincides with the emergence of orbital ferromagnetism. Combined with the
angular dependence of the superconducting diode effect, our findings uncover a
direct link between rotational and time-reversal symmetry breaking. These
symmetry requirements point towards the exchange-driven instabilities in the
momentum space as a possible origin for transport nonreciprocity in tTLG.
