**Input:** A qubit in an arbitrary state $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$.

**Goal:** Use several phase shift gates to apply the transformation represented by the following matrix to the given qubit:

$$\begin{bmatrix} 1 & 0 \\ 0 & e^{3i\pi/4} \end{bmatrix}$$
