KöMaL 2023 B5289

Let $a$, $b$, $c$ and $d$ denote non-negative real numbers such that $a+b+c+d=1$. Prove that $\frac{1}{a^2+1}+\frac{1}{b^2+1}+\frac{1}{c^2+1}+\frac{1}{d^2+1} \ge \frac72.$