Answer
$\Delta t=1.81\times10^8years$
Work Step by Step
We know the angular speed of the sun $\overline\omega=1.1\times10^{-15}s$
To make one revolution, or $\Delta\theta=2\pi rad$, the time it takes the Sun is $$\Delta t=\frac{\Delta\theta}{\overline\omega}=5.712\times10^{15}s$$
In years, that is $$\Delta t=(5.712\times10^{15}s)\Big(\frac{1min}{60s}\Big)\Big(\frac{1hr}{60min}\Big)\Big(\frac{1day}{24hr}\Big)\Big(\frac{1yr}{365.25days}\Big)$$ $$\Delta t=1.81\times10^8years$$
