Is $\theta_{23}$ maximal, and if not, in which octant?
In plain words
Muon-type and tau-type neutrinos are mixed in nearly equal amounts, but it is unknown whether the mixing angle is exactly 45 degrees or slightly above or below it. Exactly 45 degrees would point to a hidden symmetry between muons and taus.
Precise statement
Determine $\sin^{2}(\theta_{23})$ in the three-flavor PMNS framework to about $\pm 0.01$ and decide at $\ge 3\sigma$ whether $\theta_{23}=45\ \mathrm{deg}$ is excluded and, if so, whether $\theta_{23}<45\ \mathrm{deg}$ (lower octant) or $>45\ \mathrm{deg}$ (upper octant). NuFit-6.0 finds local minima near $\sin^{2}(\theta_{23})\sim 0.47$ and $\sim 0.56$ separated by $\Delta \chi^{2}<4$ for both mass orderings and both data variants (approximate).
What would settle it
DUNE and Hyper-Kamiokande $\nu_{\mu}$ disappearance and $\nu_{e}$ appearance data, using the reactor value of $\theta_{13}$, combined with atmospheric data from IceCube and KM3NeT/ORCA.
Status in the literature
Unverified note
NuFit-6.0 (2024) leaves the octant unresolved, with the other-octant minimum always within $\Delta \chi^{2} < 4$.