From Förberedande kurs i matematik 1

Because the triangle is isosceles (two sides have the same length), it can be divided up into two right-angled triangles of the same size by introducing a side which divides the angle v in half.

If we look at one of the triangles, we can set up the trigonometrical relation

\displaystyle \sin\frac{v}{2} = \frac{1}{3}\,,

which is an equation for v.