  Results from the experiments like LSND, and MiniBooNE hint towards the
possible presence of an extra eV scale sterile neutrino. The addition of such a
neutrino will significantly impact the standard three flavour neutrino
oscillations; in particular, it can give rise to additional degeneracies due to
new sterile parameters. In our work, we investigate how the sensitivity to
determine the octant of the neutrino mixing angle $\theta_{23}$ is affected by
introducing a sterile neutrino to the standard neutrino oscillation framework.
We compute the oscillation probabilities in presence of a sterile neutrino,
analytically, using the approximation that $\Delta_{21}$, the smallest mass
squared difference, is zero. We use these probabilities to understand the
degeneracies analytically at different baselines. We present our results of the
sensitivity to octant of $\theta_{23}$ for beam neutrinos using a liquid argon
time projection chamber (LArTPC). We also obtain octant sensitivity using
atmospheric neutrinos using the same LArTPC detector without any charge
identification capability. In addition, we include the charge tagging
capability of muon capture in argon which allows one to differentiate between
muon neutrino and antineutrino events. The combined sensitivity of beam and
atmospheric neutrinos in a similar experimental setup is also delineated. We
observe that by combining simulated data from the beam and atmospheric
neutrinos (including charge-id for muons), the sensitivity to the octant of
$\theta_{23}$ for true values of $\theta_{23}=41^\circ(49^\circ)$ exceeds
$4\sigma(3\sigma)$ for more than $50\%$ values of true $\delta_{13}$.
