Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays η → (π^0)(π^+)(π^-) and η → (π^0)(π^0)(π^0). As subtraction to the dispersion relation we take the one-loop chiral perturbation theory result of Gasser and Leutwyler. The calculated corrections are moderate and amount to about 14% in the amplitude at the center of the decay region. A careful analysis of the errors inherent to our approach is given. As a consequence, the experimental rate of the decay can only be reproduced if the double quark mass ratio Q^(-2) ≡ (m_d - m_u)/(m_s - m̂) * (m_d + m_u)/(m_s + m̂) is increased from the usual value of 1/(24.1)^2 to 1/(22.4 ± 0.9)^2. We have also calculated the ratio of the rates of the two decays and various Dalitz Plot parameters. In particular, the linear slope a in the charged decay is different from the one-loop value and agrees better with experiment
