Let $a > 0$, $I = [-a,a]$, and $f(x) = \dfrac{1}{1+x^2}$ for $x \in \mathbb{R}$. For all $n \in \mathbb{N}^*$, the Chebyshev points of order $n$ in $I$ are $a_{k,n}^* = a\cos\left(\frac{(2k-1)\pi}{2n}\right)$ for $k \in \llbracket 1,n \rrbracket$, and $\Pi_n^*(f)$ denotes the interpolation polynomial of $f$ at these points. Show that, if $a < 2$, the sequence $\left( \Pi _ { n } ^ { * } ( f ) \right) _ { n \in \mathbb { N } ^ { * } }$ converges uniformly towards $f$ on $[ - a , a ]$.