If the function $f\left(x\right)=\left\{\begin{array}{ccc}{\left[\tan \left(\frac{\pi }{4}+x\right)\right]}^{\frac{1}{x}}& \mathrm{f}\mathrm{o}\mathrm{r}& x\ne 0\\ k& \mathrm{f}\mathrm{o}\mathrm{r}& x=0\end{array}\right.$ is continuous at $x=0,$ then $k=?$