  The nature of the pseudogap phase remains a major barrier to our
understanding of cuprate high-temperature superconductivity. Whether or not
this metallic phase is defined by any of the reported broken symmetries, the
topology of its Fermi surface remains a fundamental open question. Here we use
angle-dependent magnetoresistance (ADMR) to measure the Fermi surface of the
cuprate Nd-LSCO. Above the critical doping $p^*$ -- outside of the pseudogap
phase -- we fit the ADMR data and extract a Fermi surface geometry that is in
quantitative agreement with angle-resolved photoemission. Below $p^*$ -- within
the pseudogap phase -- the ADMR is qualitatively different, revealing a clear
transformation of the Fermi surface. Changes in the quasiparticle lifetime
across $p^*$ are ruled out as the cause of this transformation. Instead we find
that our data are most consistent with a reconstruction of the Fermi surface by
a $Q=(\pi, \pi)$ wavevector.
