The systematic large N_c limit within chiral perturbation provides an optimal eta-eta' mixing angle of about -27 degrees at leading order in p^2. In this frame, agreement with the data can be reached with higher order corrections of about 20%. Comment: 12 pages, 2 figures; reference to the two-mixing-angle scheme added, minor corrections; to appear in JHEP
Degrande, C., & Gérard, J.-M. (2009). A Theoretical determination of the eta - eta-prime mixing. The Journal of High Energy Physics (Online), 0905, 43. https://doi.org/10.1088/1126-6708/2009/05/043 (Original work published 2009)