How to calculate $\theta$ when we know $\tan \theta$. Hej
I'm having difficulties calculating the angle given the tangent.
Example:
In a homework assignement I'm to express a complex variable $z = \sqrt{3} -i$ in polar form. I know how to solve this except for when I get to calculating the angle $\theta$.
I know that $\tan \theta = -\frac{1}{\sqrt{3}}$  but I do not know how to continue and compute the angle from that.

$$\tan\theta=\frac{-1}{\sqrt3}=\pm\frac{\frac12}{\frac{\sqrt3}2}\implies\theta=\arctan\frac{-1}{\sqrt3}=\ldots$$
Remember though that
$$\sin\frac\pi6=\frac12\;,\;\;\cos\frac\pi6=\frac{\sqrt3}2$$
and since the minus sign belongs to the imaginary part (i.e., to the sine), it must be that
$$\theta=-\frac\pi6+2k\pi\;,\;\;k\in\Bbb Z$$
