CGMO 2017 Problem 3

Given $a_i\ge 0,x_i\in\mathbb{R},(i=1,2,\ldots,n)$ . Prove that $$((1-\sum_{i=1}^n a_i\cos x_i)^2+(1-\sum_{i=1}^n a_i\sin x_i)^2)^2\ge 4(1-\sum_{i=1}^n a_i)^3$$