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At present the three major unknowns in neutrino oscillation parameters arethe mass hierarchy, the octant of $\theta_{23}$ and the CP phase $\delta_{CP}$.It is well known that the presence of hierarchy$-\delta_{CP}$ and octantdegeneracies affects the unambiguous determination of these parameters. In thispaper we show that a comprehensive way to study the remaining parameterdegeneracies is in the form of a generalized hierarchy-$\theta_{23}$ -$\delta_{CP}$ degeneracy. We show that the wrong-hierarchy and/or wrong-octantsolutions can be further classified into eight different solutions depending onwhether they occur with the wrong or right value of $\delta_{CP}$. These eightsolutions are different from the original eightfold degenerate solutions andcan exist, in principle, even if $\theta_{13}$ is known. These multiplesolutions, apart from affecting the determination of the true hierarchy andoctant, also affect the accurate estimation of $\delta_{CP}$. We identify whichof these eight different degenerate solutions can occur in the test($\theta_{23} - \delta_{CP}$) parameter space, taking the long-baselineexperiment NO$\nu$A running in the neutrino mode as an example. The inclusionof the NO$\nu$A antineutrino run removes the wrong-octant solutions appearingwith both right and wrong hierarchy. Adding T2K data to this resolves the wronghierarchy -- right octant solutions to a large extent. The remaining wronghierarchy solutions can be removed by combining NO$\nu$A + T2K with atmosphericneutrino data. We demonstrate this using ICAL@INO as the prototype atmosphericneutrino detector. We find that the degeneracies can be resolved at the$2\sigma$ level by the combined data set, for the true parameter spaceconsidered in the study.

New look at the degeneracies in the neutrino oscillation parameters, and their resolution by T2K, NO$\nu$A and ICAL