Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetries

While calculations are unchanged w.r.t. arXiv 0705-1237, the horizontal symmetries controlling the mixing angles have been uncovered, motivating a change of title and a new entry in the arXiv. A new point of view about which angles are measured has also been adopted.We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing angles; on the other hand, a neutrino-like pattern in which theta_{23} is maximal and tan (2 theta_{12}) = 2. The latter turns out to exactly satisfy the ``quark-lepton complementarity condition'' theta_c + theta_{12} = pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise, which satisfy the bound sin^2(theta_{13}) \leq 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717