\(\Leftrightarrow\left[{}\begin{matrix}tan\left(x+1\right)=\sqrt{3}\\tan\left(x+1\right)=-\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=\frac{\pi}{3}+k\pi\\x+1=-\frac{\pi}{3}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1+\frac{\pi}{3}+k\pi\\x=-1-\frac{\pi}{3}+k\pi\end{matrix}\right.\)