Using measured branching fraction of the decay J/ψ → ηY (2175)) → ηφf 0 (980) → ηφπ + π − from the BESIII experiment, we estimate branching fraction of J/ψ → ηY (2175)) → ηφf 0 (980) → ηφηπ 0 decay, which proceeds via the f 0 (980)-a 0 0 (980) mixing and the π 0 -η mixing. The branching fraction is predicted to be about O(10 −6 ), which can be accessed with 10 10 J/ψ events collected at the BESIII. The decay is dominated by the contribution from f 0 (980)-a 0 0 (980) mixing. We find that the interference between the amplitudes due to f 0 (980)-a 0 0 (980) mixing and that due to π 0 -η mixing is destructive. The branching fraction can be decreased by about 10% owing to the interference effect. We also study the ηπ 0 mass squared spectrum, and find that a narrow peak due to the f 0 (980)-a 0 0 (980) mixing in the ηπ 0 mass squared spectrum should be observed. The observation of this