ok, so you want us to find theta when [tex]cos(\theta)=\frac{\sqrt{2}}{2}[/tex]
we know from our unit circle that when the angle is 45 degrees, cos(45°)=sin(45°)=[tex]\frac{\sqrt{2}}{2}[/tex]
also we can find this by the special 45-45-90 triangle
when Θ=45°, cos(Θ)=[tex]\frac{\sqrt{2}}{2}[/tex]