Answer
\[
\pi / 4=\theta
\]
Work Step by Step
For two vectors $\vec{u}, \vec{v}$ in 3d-space, we have that:
\[
\begin{aligned}
\|\vec{v} \times \vec{u}\| &=\|\vec{v}\|\|\vec{u}\| \sin \theta \Rightarrow \sin \theta=\frac{\|\vec{u} \times \vec{v}\|}{\|\vec{u}\|\|\vec{v}\|} \\
\vec{u} \cdot \vec{v} &=\|\vec{u}\|\|\vec{v}\| \cos \theta \Rightarrow \cos \theta=\frac{\vec{u} \cdot \vec{v}}{\|\vec{u}\|\|\vec{v}\|}
\end{aligned}
\]
Where $\theta$ is the angle between $\vec{u}$ and $\vec{v}$; since $\vec{u} \cdot \vec{v}=\|\vec{u} \times \vec{v}\|$, we get that
\[
\begin{aligned}
\frac{\vec{u} \cdot \vec{v}}{\|\vec{u}\|\|\vec{v}\|}=\frac{\|\vec{u} \times \vec{v}\|}{\|\vec{u}\|\|\vec{v}\|} & \Rightarrow \sin \theta=\cos \theta \\
& \Rightarrow 1=\tan \theta \\
& \Rightarrow \frac{\pi}{4}=\theta
\end{aligned}
\]
So, the angle between $\vec{v}$, $\vec{u}$ is $\frac{\pi}{4}$
