  Given a field $F$ of characteristic $3$ and division symbol $p$-algebras
$[\alpha,\beta)_{3,F}$ and $[\alpha,\gamma)_{3,F}$ of degree $3$ over $F$, we
prove that if $\alpha \text{dlog}(\beta)\wedge \text{dlog}(\gamma)$ is trivial
in the Kato-Milne cohomology group $H_3^3(F)$ then the algebras share a common
splitting field which is an inseparable degree 3 extension of either $F$ or a
quadratic extension of $F$. In the special case of quadratically closed fields,
if $\alpha \text{dlog}(\beta)\wedge \text{dlog}(\gamma)=0$, then they share an
inseparable degree 3 extension of $F$.
