The search for a new source of CP violation is one of the most important endeavors in particle physics. A particularly interesting way to perform this search is to probe the CP phase in the $htautau$ coupling, as the phase is currently completely unconstrained by all existing data. Recently, a novel variable $Theta$ was proposed for measuring the CP phase in the $htautau$ coupling through the $tau^pm to pi^pm pi^0 u$ decay mode. We examine two crucial questions that the real LHC detectors must face, namely, the issue of neutrino reconstruction and the effects of finite detector resolution. For the former, we find strong evidence that the collinear approximation is the best for the $Theta$ variable. For the latter, we find that the angular resolution is actually not an issue even though the reconstruction of $Theta$ requires resolving the highly collimated $pi^pm$s and $pi^0$s from the $tau$ decays. Instead, we find that it is the missing transverse energy resolution that significantly limits the LHC reach for measuring the CP phase via $Theta$. With the current missing energy resolution, we find that with $sim 1000,textrm{fb}^{-1}$ the CP phase hypotheses $Delta = 0^circ$ (the standard model value) and $Delta = 90^circ$ can be distinguished, at most, at the 95% confidence level.
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