CN-LEAGUE 2012 Problem 9

Given a function $f(x)=a\sin x-\frac{1}{2}\cos 2x+a-\frac{3}{a}+\frac{1}{2}$ , where $a\in\mathbb{R}, a\ne 0$ . (1) If for any $x\in\mathbb{R}$ , inequality $f(x)\le 0$ holds, find all possible value of $a$ .(2) If $a\ge 2$ , and there exists $x\in\mathbb{R}$ , such that $f(x)\le 0$ . Find all possible value of $a$ .