  NGC300 X-1 and IC10 X-1 are currently the only two robust extragalactic
candidates for being Wolf-Rayet/black hole X-ray binaries, the Galactic
analogue being Cyg X-3. These systems are believed to be a late product of
high-mass X-ray binary evolution and direct progenitors of black hole mergers.
From the analysis of Swift data, the orbital period of NGC 300 X-1 was found to
be 32.8h. We here merge the full set of existing data of NGC300 X-1, using
XMM-Newton, Chandra and Swift observations to derive a more precise value of
the orbital period of 32.7932+-0.0029h above a confidence level of 99.99%. This
allows us to phase connect the X-ray light curve of the source with radial
velocity measurements of He II lines performed in 2010. We show that, as for
IC10 X-1 and Cyg X-3, the X-ray eclipse corresponds to maximum of the blueshift
of the He II lines, instead of the expected zero velocity. This indicates that
for NGC300 X-1 as well, the wind of the WR star is completely ionised by the
black hole radiation and that the emission lines come from the region of the WR
star that is in the shadow. We also present for the first time the light curve
of two recent very long XMM-Newton observations of the source, performed on the
16th to 20th of December 2016.
