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We have measured the radiative decays φ→ηγ, φ→η′γ selecting π+π−γγγ final state in a sample of ∼5×107 φ-mesons produced at the Frascati φ-factory DAΦNE. We obtain Γ(φ→η′γ)/Γ(φ→ηγ)=(4.70±0.47±0.31)×10−3. From this result we derive new accurate values for the branching ratio BR(φ→η′γ)=(6.10±0.61±0.43)×10−5 and the mixing angle of pseudoscalar mesons in the flavour basis ϕP=(41.8+1.9−1.6)°. [Copyright &y& Elsevier]