Can we measure $\theta_{23}$ octant in 3+1 scheme?

Current 3$\nu$ global fits predict two degenerate solutions for $\theta_{23}$: one lies in lower octant ($\theta_{23} <\pi/4$), and the other belongs to higher octant ($\theta_{23} >\pi/4$). Here, we study how the measurement of $\theta_{23}$ octant would be affected in the upcoming Deep Underground Neutrino Experiment (DUNE) if there exist a light eV-scale sterile neutrino. We show that in 3+1 scheme, a new interference term in $\nu_\mu \to \nu_e$ oscillation probability can spoil the chances of measuring $\theta_{23}$ octant completely.