  The octant of $\theta_{23}$ and $\delta_{CP}$ are the two major unknowns in
neutrino oscillation physics. The precise determination of octant and
$\delta_{CP}$ is interlinked through the octant-$\delta_{CP}$ degeneracy. In
this paper we study the proficiency of the DUNE experiment to determine these
parameters, in particular, the role played by the antineutrinos, the broadband
nature of the beam and the matter effect. For $P_{\mu e}$ and $P_{\bar{\mu}
\bar{e}}$ the octant-$\delta_{CP}$ degeneracy occurs at different values of
$\delta_{CP}$, combination of neutrino and antineutrino runs help to resolve
this. However, in regions where neutrinos do not have octant degeneracy adding
antineutrino data is expected to decrease the sensitivity because of the
degeneracy and reduced statistics. However we find that in case of DUNE
baseline, the antineutrino runs help even in parameter space where the
antineutrino probabilities suffer from degeneracies. We explore this point in
detail and point out that this happens because of the (i) broad-band nature of
the beam so that even if there is degeneracy at a particular energy bin, over
the whole spectrum the degeneracy may not be there; (ii) the enhanced matter
effect due to the comparatively longer baseline which creates an increased
tension between the neutrino and the antineutrino probabilities which raises
the overall $\chi^2$ in case of combined runs. This feature is more prominent
for IH since the antineutrino probabilities in this case are much higher than
the neutrino probabilities due to matter effects. The main role of
antineutrinos in enhancing CP sensitivity is their ability to remove the
octant-$\delta_{CP}$ degeneracy. However even if one assumes octant to be known
the addition of antineutrinos can give enhanced CP sensitivity in some
parameter regions due to the tension between the neutrino and antineutrino
$\chi^2$s.
