  The second- and third-order azimuthal anisotropy Fourier harmonics of charged
particles produced in pPb collisions, at $\sqrt{s_\mathrm{NN}} =$ 8.16 TeV, are
studied over a wide range of event multiplicities. Multiparticle correlations
are used to isolate global properties stemming from the collision overlap
geometry. The second-order "elliptic" harmonic moment is obtained with high
precision through four-, six-, and eight-particle correlations and, for the
first time, the third-order "triangular" harmonic moment is studied using
four-particle correlations. A sample of peripheral PbPb collisions at
$\sqrt{s_\mathrm{NN}} =$ 5.02 TeV that covers a similar range of event
multiplicities as the pPb results is also analyzed. Model calculations of
initial-state fluctuations in pPb and PbPb collisions can be directly compared
to the high precision experimental results. This work provides new insight into
the fluctuation-driven origin of the $v_3$ coefficients in pPb and PbPb
collisions, and into the dominating overall collision geometry in PbPb
collisions at the earliest stages of heavy ion interactions.
