If is a solution then and must lie at the intersections of some horizontal line through the unit circle. Furthermore, the angle between these points (measured from the origin) must be . But the other angles between the rightmost point and the positive x axis and the leftmost point and the negative x axis must be equal by symmetry, so call them .
This leads to the equation , since together the three angles make a straight line. This gives you one solution and then the other is easily found.
gives the y co-ordinate of a point on the Unit Circle,
hence the y-axis from to acts as an axis of symmetry.
requires that and are either side of the y-axis.
The exact same logic may be used underneath the x-axis for
to obtain a 2nd solution.
Complete the analysis by adding multiples of 360 degrees to the two solutions.