ctg(1/2arccos(-1/3)) срооочно плз помогите !!)))

Решите задачу:

$ctg(\frac{arccos(-\frac{1}{3})}{2})\\ ctg\frac{a}{2} = \frac{1+cosa}{sina}=\frac{1+cos*(arccos(-\frac{1}{3}))}{sina(arccos(-\frac{1}{3}))}=\\ arccos(-\frac{1}{3})=x\\ cosx= - \frac{1}{3}\\ sinx=\sqrt{1-\frac{1}{9}}=\frac{\sqrt{8}}{3}\\ x=arcsin(\frac{\sqrt{8}}{3})\\ ctg(\frac{arccos(-\frac{1}{3})}{2}) = \frac{ 1-\frac{1}{3}}{\frac{\sqrt{8}}{3}} = \frac{2}{\sqrt{8}}=\frac{\sqrt{2}}{2}$