  After the landmark discovery of non-zero $\theta_{13}$ by the modern reactor
experiments, unprecedented precision on neutrino mass-mixing parameters has
been achieved over the past decade. This has set the stage for the discovery of
leptonic CP violation (LCPV) at high confidence level in the next-generation
long-baseline neutrino oscillation experiments. In this work, we explore in
detail the possible complementarity among the on-axis DUNE and off-axis T2HK
experiments to enhance the sensitivity to LCPV suppressing the
$\theta_{23}-\delta_{\mathrm{CP}}$ degeneracy. We find that none of these
experiments individually can achieve the milestone of 3$\sigma$ LCPV for at
least 75% choices of $\delta_{\mathrm{CP}}$ in its entire range of
$[-180^{\circ} , 180^{\circ}]$, with their nominal exposures and systematic
uncertainties. However, their combination can attain the same for all values of
$\theta_{23}$ with only half of their nominal exposures. We observe that the
proposed T2HKK setup in combination with DUNE can further increase the CP
coverage to more than 80% with only half of their nominal exposures. We study
in detail how the coverage in $\delta_{\mathrm{CP}}$ for $\ge$ 3$\sigma$ LCPV
depends on the choice of $\theta_{23}$, exposure, optimal runtime in neutrino
and antineutrino modes, and systematic uncertainties in these experiments in
isolation and combination. We find that with an improved systematic uncertainty
of 2.7% in appearance mode, the standalone T2HK setup can provide a CP coverage
of around 75% for all values of $\theta_{23}$. We also discuss the pivotal role
of intrinsic, extrinsic, and total CP asymmetries in the appearance channel and
extrinsic CP asymmetries in the disappearance channel while analyzing our
results.
