Recent global fit analyses of world oscillation data under 3ν hypothesis show a preference for normal mass ordering (NMO) at 2.5σ and provide 1.6σ indications for lower θ 23 octant (sin 2 θ 23 < 0.5) and leptonic CP violation (sin δ CP < 0). A high-precision measurement of 2-3 mixing angle is pivotal to convert these hints into discoveries and to address the long-standing flavor problem. In this work, we study in detail the capabilities of the long-baseline experiment DUNE to establish the deviation from maximal θ 23 and to resolve its octant at high confidence levels in light of the current neutrino oscillation data. We exhibit the possible correlations and degeneracies among sin 2 θ 23 , ∆m 2 31 , and δ CP in ν µ → ν µ and ν µ → ν e oscillation channels at the probability and event levels. Introducing for the first time, a bi-events plot in the plane of total ν and ν disappearance events, we discuss the impact of sin 2 θ 23 -∆m 2 31 degeneracy in establishing non-maximal θ 23 and show how this degeneracy can be resolved by exploiting the spectral shape information in ν and ν disappearance events. A 3σ (5σ) determination of non-maximal θ 23 is possible in DUNE with an exposure of 336 kt•MW•years if the true value of sin 2 θ 23 0.465 (0.450) or sin 2 θ 23 0.554 (0.572) for any value of true δ CP and true NMO. We study the individual contributions from appearance and disappearance channels, impact of systematic uncertainties and marginalization over oscillation parameters, importance of spectral analysis and data from both ν and ν runs, while analyzing DUNE's sensitivity for the discovery of a non-maximal θ 23 . We observe that both ν and ν data are essential to settle the θ 23 octant at a high confidence level. DUNE can resolve the octant of θ 23 at 4.2σ (5σ) using 336 (480) kt•MW•years of exposure assuming the present best-fit values of sin 2 θ 23 (0.455) and δ CP (223 • ) as their true choices and with true NMO. DUNE can improve the current relative 1σ precision on sin 2 θ 23 (∆m 2 31 ) by a factor of 4.4 (2.8) using 336 kt•MW•years of exposure.