[tex]\displaystyle\bf\\\frac{6}{2Sin\alpha Cos\alpha +Cos2\alpha \cdot Ctg2\alpha } \cdot\frac{1}{2Sin2\alpha } =\\\\\\=\frac{6}{Sin2\alpha+Cos2\alpha \cdot \frac{Cos2\alpha }{Sin2\alpha } } \cdot\frac{1}{2Sin2\alpha } =\\\\\\=\frac{6Sin2\alpha }{Sin^{2} 2\alpha +Cos^{2} 2\alpha }\cdot\frac{1}{2Sin2\alpha } =\frac{6Sin2\alpha }{1} \cdot\frac{1}{2Sin2\alpha } =3[/tex]