Lets look at the equations
$$\frac{d}{dt}\left(\mathbf I\,\vec\omega\right)=\vec\tau$$
if the torque $~\vec\tau~$ is equal zero then the momentum
$$\vec L=\mathbf I\,\vec\omega=\vec c$$ where $\vec c$ is constant
the angle between $~\vec L~$ and $~\vec\omega~$ is proportional to the $~\vec \omega ^T\,\vec L$ thus
$$\theta_1\propto \vec\omega^T\,\mathbf I\,\vec\omega\propto \vec\omega^T\vec c\tag 1$$
if the torque is not equal zero then
$$\vec L=\mathbf I\,\vec\omega=\int \vec\tau\,dt=\vec f(t)$$ and the angle is now
$$\theta_2\propto \vec\omega^T\vec f(t)\tag 2$$
thus angle $~\theta_1\ne \theta_2$
$$\cos(\theta)=\frac{\vec a^T\,\vec b}{a\,b}$$