Space rotation/z-Axis/45 degree/Respect to (1,2,4), (3,3,-1), (5,0,7)/Exercise

Let

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3}$

be the space rotation by ${}45$ degree aroand the ${}z$-axis counterclockwise. How does the matrix describing ${}\varphi$ with respect to the basis

${\begin{pmatrix}1\\2\\4\end{pmatrix}},\,{\begin{pmatrix}3\\3\\-1\end{pmatrix}},\,{\begin{pmatrix}5\\0\\7\end{pmatrix}}$

look like?

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