AT-OEMO-REG 2016 Problem 2

Let $a$ , $b$ , $c$ and $d$ be real numbers with $a^2 + b^2 + c^2 + d^2 = 4$ . Prove that the inequality $$(a+2)(b+2) \ge cd$$ holds and give four numbers $a$ , $b$ , $c$ and $d$ such that equality holds.

(Walther Janous)