Two Sevenths as Pandigital Fraction

Theorem

There are $6$ ways $\dfrac 2 7$ can be expressed as a pandigital fraction:

$\dfrac 2 7 = \dfrac {3654} {12789}$

$\dfrac 2 7 = \dfrac {3674} {12859}$

$\dfrac 2 7 = \dfrac {5342} {18697}$

$\dfrac 2 7 = \dfrac {7418} {25963}$

$\dfrac 2 7 = \dfrac {9786} {34251}$

$\dfrac 2 7 = \dfrac {9862} {34517}$

Proof

Can be verified by brute force.