Let $\displaystyle E_{n} = $\{$x $\in$ $\[0,2$\pi$]$ : (sin(nx))/n > 0$\}$$ with n natural number.

Calculate: E', E'' where E' = liminf E_{n}, E'' = limsup E_{n}for n that goes to $\displaystyle $\infty$$

Looking at the goniomethrical discus i should say that liminf is the empty set and that limsup is $\displaystyle [0,2$\pi$]$ \$\displaystyle \{0,$\pi$, 2$\pi$\}$, but how could i formalize it (if is correct) ?