Express $-1-i$ in polar form with principal value of the amplitude.

$$\begin{gathered} -1-i=r\left(\cos \theta +i\sin \theta \right)\Rightarrow r^2=2, \Rightarrow r=\sqrt{2} \\ r \cos \theta =-1, r \sin \theta =-1 \\ \cos \theta =-\frac{1}{\sqrt{2}}, \sin \theta =-\frac{1}{\sqrt{2}}, \\ \theta \in Q_3 -\pi <\theta \le \pi , \end{gathered}$$

the value of $\theta$ satisfying the equations

$\cos \theta =-\frac{1}{\sqrt{2}}, \sin \theta =-\frac{1}{\sqrt{2}}is \theta =\frac{-3\pi }{4}$