Degenerate fourfold Massey products over arbitrary fields

We prove that, for all fields F of characteristic different from 2 and all a,b,c\in F^{\times} , the mod 2 Massey product \langle a,b,c,a\rangle vanishes as soon as it is defined. For every field F_{0} , we construct a field F containing F_{0} and a,b,c,d\in F^{\times} such that \langle a,b,c\rangle and \langle b,c,d\rangle vanish but \langle a,b,c,d\rangle is not defined. As a consequence, we answer a question of Positselski by constructing the first examples of fields containing all roots of unity and such that the mod 2 cochain differential graded algebra of the absolute Galois group is not formal.