Let $G=\langle\mu\rangle$ be the subgroup of $S_4$, now compute the coset of $G$ using...?
Hint: Cosets of any group by any subgroup partition the group . . .
. . . and so each element of the desired cosets of $G$ is in exactly one coset; namely, $G\begin{pmatrix} 1 & 2 & 3 & 4\\ 4 & 3 & 2 & 1 \end{pmatrix}$.