  For $x$ an element of a field other than $0$ or $1$, we compute the order $n$
Massey products $$\langle (1-x)^{-1}, x^{-1}, \ldots, x^{-1}, (1-x)^{-1}
\rangle$$ of $n-2$ factors of $x^{-1}$ and two factors of $(1-x)^{-1}$ by
embedding $\mathbb{P}^1 - \{0,1,\infty\}$ into its Picard variety and
constructing $\operatorname{Gal}(k^s/k)$ equivariant maps from $\pi_1$ applied
to this embedding to unipotent matrix groups. This method produces obstructions
to $\pi_1$-sections of $\mathbb{P}^1 - \{0,1,\infty\}$, partial computations of
obstructions of Jordan Ellenberg, and also computes the Massey products
$$\langle x^{-1} , (-x)^{-1}, \ldots, (-x)^{-1}, x^{-1} \rangle.$$
