Polar Form of a Complex Number

Algebra Level 3

The complex number $x= \sqrt{3} - i$ can be expressed in polar form $x = r\left(\cos\theta + i\sin\theta \right)$ , where $r$ is a positive real number and $0 \leq \theta \leq 2\pi$ . In fact, $\theta = \frac{a\pi}{b}$ where $a$ and $b$ are coprime positive integers. What is the value of $a+b$ ?

Details and assumptions

$i$ is the imaginary unit, where $i^2=-1$ .