= Solution
Write $\boldsymbol\omega=(\omega_x,\omega_y,\omega_z)$. The <cross product> gives $\mathbf v=(\omega_yz-\omega_zy,\omega_zx-\omega_xz,\omega_xy-\omega_yx)$. Since the components of $\boldsymbol\omega$ are constant, direct <partial differentiation> gives
$$
\nabla\times\mathbf v=(\omega_x-(-\omega_x),\omega_y-(-\omega_y),\omega_z-(-\omega_z))=2\boldsymbol\omega.
$$
Thus
$$
\boxed{\boldsymbol\omega=\tfrac12\nabla\times\mathbf v.}
$$
The <vorticity> is twice the local angular velocity of this rigid-body rotation.
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