  We use a model, with no CP violation, of the world's neutrino oscillation
data, excluding the LSND experiments, and search the full parameter space
($0\leq\theta_{12} \le \pi/2$; $-\pi/2 \le \theta_{13} \le \pi/2$; and
0\leq\theta_{23} \le \pi /2$) for the best fit values of the mixing angles and
mass-squared differences. We find that the mixing angle $\theta_{13}$ is
bounded by $-0.15<\theta_{13}<0.20$ with an absolute minimum at
$\theta_{13}=0.12$ and a local minimum at $-0.04$. The importance of the
negative $\theta_{13}$ region and this structure in the chi-square space has
heretofore been overlooked because the factorization approximation commonly
employed yields oscillation probabilities that are a function of
$\sin^2\theta_{13}$.
