An extended $U(3)_Lbigotimes U(3)_R$ chiral theory which includes pseudoscalar and vector meson nonets as dynamic degrees of freedom is presented. We combine a hidden symmetry approach with a general procedure of including the $eta$ meson into chiral theory. The $U(3)_Lbigotimes U(3)_R$ and the SU(3) symmetries are broken by the mechanism based on quark mass matrix. Meson radiative decay widths are parameterized in terms of a single and real $eta-eta$ mixing angle $theta_P$, a U(3)_V symmetry breaking scale parameter c_W, and the radiative decay constants $F_pi, F_K, F_eta, F_{eta}$, for the $pi, eta$, K, $eta $ mesons, respectively. Taking $F_pi = 93 MeV$, a global fit to decay width data yields F_K/F_pi = 1.16 pm 0.11, F_eta/F_pi = 1.14pm 0.04, F_{eta}/F_pi = 1.09 pm 0.04, c_W = -0.19 pm0.03, theta_P =-(15.4 pm 1.8)^o.
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