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Global analyses [1-3] of the existing neutrino oscillation data point to near--percent-level relative $1\sigma$-precision in oscillation parameters such as $\vert \Delta m^2_{31} \vert $ $ \left(1.1\%\right)$, $\Delta m^2_{21} $ $ \left(2.3\%\right)$, $\sin^2\theta_{13} $ $\left(3.0\%\right)$ and $\sin^2\theta_{12}\left(4.5\%\right)$. All these analyses show a preference for the normal mass ordering, thus disfavoring the inverted mass ordering at nearly $\sim 2.5\sigma$. Refs. [1] and [2] find the best fit for $\theta_{23}$ in the higher octant at $\sin^2\theta_{23}\sim 0.57$ while Ref. [3] finds the best fit for $\theta_{23}$ in the lower octant at $\sin^2\theta_{23}\sim 0.46$. All three of them allow the solution in the other octant at $2\sigma$ or less. It should also be noted that all these analyses allow maximal 2-3 mixing i.e. the value $\sin^2\theta_{23} = 0.5$ at $\sim$ $2.5\sigma$ or less. The primary goal of the next-generation experiments such as the Deep Underground Neutrino Experiment (DUNE) [4] is to {\it conclusively} find out the sign of $m^2_{3} - m^2_{1}$, the value of $\sin^2\theta_{23}$, the existence of leptonic CP-violation in neutrino sector and the value of its phase $\delta_{\rm CP}$. The main aim of this work is to explore if DUNE can conclusively rule-out maximal 2-3 mixing if the true $1\sigma$ range of $\sin^2\theta_{23}$ is $\sim\left(0.44,~0.47\right)$ as indicated in Ref. [3]. Our work highlights that while this measurement is, by and large, independent of the systematic uncertainties and an imprecise understanding of $\delta_{\rm CP}$; it crucially depends on performing a spectral analysis to resolve the $\vert \Delta m^2_{31} \vert$--$\sin^2\theta_{23}$ degeneracy - a feature that can potentially ruin DUNE's sensitivity for $\sin^2\theta_{23}$ resolution if $\vert \Delta m^2_{31} \vert$ is not known accurately-enough. We find that disappearance data from DUNE can improve the current precision in the measurements of $\vert \Delta m^2_{31} \vert$ and $\sin^22\theta_{23}$ by a factor of three while the appearance data can very effectively eliminate the wrong-octant solution. {\it Our results show that DUNE can exclude $\sin^2\theta_{23}=0.5$ at $\sim 2\sigma$ for the current $1\sigma$-upper bound of $\sin^2\theta_{23}\sim 0.47$. For the current best-fit of $\sin^2\theta_{23}=0.455$, a $\sim 4\sigma$ exclusion is possible.