A recent paper based on data from the T2K experiment which observed electron neutrinos in a muon neutrino beam touts in its abstract the unremarkable and well proven fact that parameter theta13 in the PMNS matrix is non-zero, which it limits to certain counter-factual or speculative assumptions about the value of other PMNS matrix parameters.
More interestingly, if their data is evaluated in light of the already fairly accurately estimated values of theta13, theta23 and the neutrino mass eigenstate differences, the T2K data show a preferences for a CP violating phase of the PMNS matrix that governs neutrino oscillation of about -pi/2 (or equivalently -90 degrees, 270 degrees, or 3/2pi aka pau). This result is insensitive to the question of whether the neutrino masses have a normal or inverted hierarchy and apparently also to the value of theta12.
This is midway between two prior efforts to make a best fit CP violation phase for the PMNS matrix, one of about 1.08pi and the other of about 1.7pi. The average of the three estimates is about 1.42pi. It is also not far removed from the CP violating phase in the CKM matrix of about 1.23pi.
All of the estimates, of course, have significant margins of uncertainty. But, the gross consistency of the three measurements does suggest that a non-zero CP violation phase for the PMNS matrix is likely, and favors one half of the allowed 0 to 2pi range over the other.