Analysis of three-neutrino oscillations in the full mixing angle space

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}$.