  The various global analyses of available neutrino oscillation data indicate
the presence of the standard $3+0$ neutrino oscillation picture. However, there
are a few short baseline anomalies that point to the possible existence of a
fourth neutrino (with mass in the eV-scale), essentially sterile in nature.
Should sterile neutrino exist in nature and its presence is not taken into
consideration properly in the analyses of neutrino data, the interference terms
arising due to the additional CP phases in presence of a sterile neutrino can
severely impact the physics searches in long baseline (LBL) neutrino
oscillation experiments. In the current work we consider one light (eV-scale)
sterile neutrino and probe all the three CP phases ($\delta_{13}$,
$\delta_{24}$, $\delta_{34}$) in the context of the upcoming Deep Underground
Neutrino Experiment (DUNE) and also estimate how the results improve when data
from NOvA, T2K and T2HK are added in the analysis. We illustrate the $\Delta
\chi^2$ correlations of the CP phases among each other, and also with the three
active-sterile mixing angles. Finally, we briefly illustrate how the relevant
parameter spaces in the context of neutrinoless double beta decay get modified
in light of the bounds in presence of a light sterile neutrino.
