I need to calculate $lim_{n\rightarrow\infty}\int_A{(|x|(1-|x|))^{(1/n)}arctg(ny)\over{1+x^2+y^2}} dxdy$, where
$A = \{w\in \Bbb{R^2}: |w|\le \sin(3\cdot \angle(w,e_1)) \}$ where $e_1=(0,1)\in \Bbb{R^2}$. I know that I have to use Lebesgue's theorem and I know that $lim_{n\rightarrow\infty}f_n=$$\pm\pi\over2(1+x^2+y^2)$ depending on $sgn(y)$. But I got problem with understanding set $A$.