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

Current 3$ u$ 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 $ u_mu to u_e$ oscillation probability can spoil the chances of measuring $theta_{23}$ octant completely.