Why measuring the octant of the atmospheric oscillation parameter of neutrinos is important? As some of you may know, the PMNS mixing angle $\theta_{23}$ has been measured to a value very close to 45°. In other words, the oscillation amplitude (2 flavour approx.) which is driven by $\sin^2(2\theta)$ is close to 1.
Nowadays, precision measurments of $\theta_{23}$ are achieved by accelerator based experiments (T2K/NO$\nu$A) and we may have a clue if wether $\theta_{23}$ belongs to the upper-octant ($> \pi/2$), the lower octant  ($< \pi/2$) or exactly $=\pi/2$.
My question is: what are the implications of the octant in particle physics?
My current understanding is that some theories can establish predictions on the octant out of some theoretical considerations. Does anyone has more information on the subject?
 A: 
In this work, we discuss how this study can be further analysed to resolve entanglement of the quadrant of leptonic CPV phase and Octant of atmospheric mixing angle θ23, at LBNEs. The study is done for both NH (Normal hierarchy) and IH (Inverted hierarchy), HO (Higher Octant) and LO (Lower Octant). We show how baryogenesis can enhance the effect of resolving this entanglement, and how possible values of the leptonic CP-violating phase δCP can be predicted in this context.

Another link:

The upcoming generation of neutrino experiments will be sensitive to subdominant neutrino oscillation effects that can in principle give information on the yet-unknown neutrino parameters: the Dirac CP-violating phase in the PMNS mixing matrix, the neutrino mass ordering and the octant of θ23. Determining the exact values of neutrino mass and mixing parameters is crucial to test various neutrino models and flavor symmetries that are designed to predict these neutrino parameters

italics mine.
You ask:

My question is: what are the implications of the octant in particle physics?

From the abstracts it seems that predicting the behavior of the octant is important both for cosmological models (baryogenesis, leptogenesis) and for the basic neutrino interaction parameters. A complicated subject, it is exploring new physics.
