Trigonometry Question

In order to cross the x axis, the graph has to be zero somewhere, that is,

$$\begin{gathered} f\left(x\right)=\sin x=0 \\ x=2n\mathrm{\pi } \mathrm{where} \mathrm{n}\in \mathrm{\mathbb{Z}} \end{gathered}$$

for $n=-1$

$x=-\mathrm{\pi }$

And for $n=2$

$x=-2\mathrm{\pi }$

Thus, we have two solutions in the interval $[-2\mathrm{\pi },0)$, those are $x=-\mathrm{\pi },-2\mathrm{\pi }$