Splitting varieties for triple Massey products

We construct splitting varieties for triple Massey products. For a,b,c∈F⁎ the triple Massey product 〈a,b,c〉 of the corresponding elements of H1(F,μ2) contains 0 if and only if there are x∈F⁎ and y∈F[a,c]⁎ such that bx2=NF[a,c]/F(y), where NF[a,c]/F denotes the norm, and F is a field of characteristic different from 2. These varieties satisfy the Hasse principle by a result of D.B. Leep and A.R. Wadsworth. This shows that triple Massey products for global fields of characteristic different from 2 always contain 0.