Given: The planet completes $2$ revolutions in $360$ days.

One rotation of the planet moves $2\pi \mathrm{radians}$ angle.

Thus, angular frequency $\omega =\frac{\theta }{t}$, where $\theta$ represents the angle moved by the object and $t$ represents the time taken by the object to travel through $\theta$.

$\omega =\frac{2\times 2\pi }{360}=0.0348=3.5\times {10}^{-2} \mathrm{rad} {\mathrm{day}}^{-1}$.