Answer
As a result $\theta=\frac{\pi}{3}$.
Work Step by Step
We are given the vecor $\langle1,\sqrt3\rangle$. If we break the vector down into components we can think of it as a right triangle with a base of $1$ and a height of $\sqrt3$. We can then apply trigonometry in order to find $\theta$.
$\tan{\theta}=\frac{\sqrt3}{1}\Rightarrow\theta=\arctan{\frac{\sqrt3}{1}}=\frac{\pi}{3}$
