Deduce that, for every polynomial $P \in \mathbb{R}[X]$, $$\lim_{n \rightarrow +\infty} \mathbb{E}\left(\frac{1}{n} \sum_{i=1}^{n} P\left(\Lambda_{i,n}\right)\right) = \frac{1}{2\pi} \int_{-2}^{2} P(x) \sqrt{4 - x^{2}} \, \mathrm{d}x$$