  At present the three major unknowns in neutrino oscillation parameters are
the 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 octant
degeneracies affects the unambiguous determination of these parameters. In this
paper we show that a comprehensive way to study the remaining parameter
degeneracies is in the form of a generalized hierarchy-$\theta_{23}$ -
$\delta_{CP}$ degeneracy. We show that the wrong-hierarchy and/or wrong-octant
solutions can be further classified into eight different solutions depending on
whether they occur with the wrong or right value of $\delta_{CP}$. These eight
solutions are different from the original eightfold degenerate solutions and
can exist, in principle, even if $\theta_{13}$ is known. These multiple
solutions, apart from affecting the determination of the true hierarchy and
octant, also affect the accurate estimation of $\delta_{CP}$. We identify which
of these eight different degenerate solutions can occur in the test
($\theta_{23} - \delta_{CP}$) parameter space, taking the long-baseline
experiment NO$\nu$A running in the neutrino mode as an example. The inclusion
of the NO$\nu$A antineutrino run removes the wrong-octant solutions appearing
with both right and wrong hierarchy. Adding T2K data to this resolves the wrong
hierarchy -- right octant solutions to a large extent. The remaining wrong
hierarchy solutions can be removed by combining NO$\nu$A + T2K with atmospheric
neutrino data. We demonstrate this using ICAL@INO as the prototype atmospheric
neutrino detector. We find that the degeneracies can be resolved at the
$2\sigma$ level by the combined data set, for the true parameter space
considered in the study.
