(ctga/3-tga/3)*tg2a/3

$(ctg \frac{ \alpha }{3} -tg \frac{ \alpha }{3} )*tg2 \frac{ \alpha }{3}$
$tg2 \frac{ \alpha }{3} = \frac{2tg \frac{ \alpha }{3} }{1-tg^2 \frac{ \alpha }{3} }$
$ctg \frac{ \alpha }{3} -tg \frac{ \alpha }{3} * \frac{2tg \frac{ \alpha }{3} }{1-tg^2 \frac{ \alpha }{3} } = \frac{2tg \frac{ \alpha }{3}(ctg\frac{ \alpha }{3}-tg\frac{ \alpha }{3}) }{1-tg^2\frac{ \alpha }{3}}$
$\frac{2ctg\frac{ \alpha }{3}*tg\frac{ \alpha }{3}-2tg^2\frac{ \alpha }{3}}{1-tg^2\frac{ \alpha }{3}} = \frac{2-2tg^2\frac{ \alpha }{3}}{1-tg^2\frac{ \alpha }{3}} = \frac{2(1-tg^2\frac{ \alpha }{3})}{(1-tg^2\frac{ \alpha }{3})} =2$

* $tg \alpha *ctg \alpha = \frac{sin \alpha }{cos \alpha } * \frac{cos \alpha }{sin \alpha } =1$