CMOQR 2022 Problem 3

Consider n real numbers $x_0, x_1, . . . , x_{n-1}$ for an integer $n \ge 2$ . Moreover, suppose that for any integer $i$ , $x_{i+n} = x_i$ . Prove that $$\sum^{n-1}_{i=0} x_i(3x_i - 4x_{i+1} + x_{i+2}) \ge 0.$$