I need to perform the measurements on a quantum circuit in the basis $\{ \eta^\pm,\zeta^\pm \} $. Where $ \eta^\pm,\zeta^\pm $ are given as follows: $$\eta^\pm = \frac{1}{2}|001\rangle + \frac{1}{2}|010\rangle \pm \frac{1}{\sqrt{2}}|100\rangle \\ \zeta^\pm = \frac{1}{2}|101\rangle + \frac{1}{2}|110\rangle \pm \frac{1}{\sqrt{2}}|000\rangle $$ How to obtain a mapping from any 4 of basis states ($|000\rangle,|001\rangle,\ldots |111\rangle$) to states $(\eta^\pm,\zeta^\pm)$? I was able to find the circuit and unitary for $\eta^\pm$ and $\zeta^\pm$ separately, but not a single unitary for mapping to all the four states.

The circuit $\eta^+$ with initial state $|000\rangle$ looks like: