You can put this solution on YOUR website! Cos (sqrt (2)/2) is at 45 degrees, or pi/4 radians. That, however is positive. It becomes negative in the second and third quadrants. Each of those is pi/2 more.
pi/4+ pi/2= 3 pi/4 That is one solution.
3pi/4+pi/2=5 pi/4 That is the other solution.
In degrees, it is 135 and 225.