We present a spectral analysis of four coordinated NuSTAR+XMM-Newton
observations of the Seyfert galaxy NGC 1365. These exhibit an extreme level of
spectral variability, which is primarily due to variable line-of-sight
absorption, revealing relatively unobscured states in this source for the first
time. Despite the diverse range of absorption states, each of the observations
displays the same characteristic signatures of relativistic reflection from the
inner accretion disk. Through time-resolved spectroscopy we find that the
strength of the relativistic iron line and the Compton reflection hump relative
to the intrinsic continuum are well correlated, as expected if they are two
aspects of the same broadband reflection spectrum. We apply self-consistent
disk reflection models to these time-resolved spectra in order to constrain the
inner disk parameters, allowing for variable, partially covering absorption to
account for the vastly different absorption states observed. Each of the four
observations is treated independently to test the consistency of the results
obtained for the black hole spin and the disk inclination, which should not
vary on observable timescales. We find both the spin and the inclination
determined from the reflection spectrum to be consistent, confirming NGC 1365
hosts a rapidly rotating black hole; in all cases the dimensionless spin
parameter is constrained to be a* > 0.97 (at 90% statistical confidence or
better)