  To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find
constraints on flavor neutrino masses M_{ij} (ij=e,\mu,\tau): C1) c_{23}^2
M_{\mu\mu} + s_{23}^2 M_{\tau\tau} \approx 2 s_{23} c_{23}M_{\mu\tau} + M_{ee}
and/or C2) |c_{23}M_{e\mu} -s_{23}M_{e\tau}|>> |s_{23}M_{e\mu}
+c_{23}M_{e\tau}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and
theta_{12}, theta_{13} and theta_{23} are the mixing angles for three flavor
neutrinos. The applicability of C1) and C2) is examined in models with one
massless neutrino and two massive neutrinos suggested by \det(M)=0, where M is
a mass matrix constructed from M_{ij} (i,j=e,\mu,\tau). To make definite
predictions on neutrino masses and mixings, especially on sin(theta_{13}), that
enable us to trace C1) and C2), M is assumed to possess texture zeros or to be
constrained by textures with M_{\mu\mu}=M_{\tau\tau} or M_{e\tau}=\pm M_{e\mu}
which turn out to ensure the emergence of the maximal atmospheric neutrino
mixing at sin(theta_{13})->0. It is found that C1) is used by textures such as
M_{e\mu}=0 or M_{e\tau}=0 while C2) is used by textures such as M_{e\tau}=\pm
M_{e\mu}.
