2arctan

Arctan is the inverse of tan.
If y = tan (x)
x = arctan(y)

Now let cos(y) = 2arctan(√2)
So, tan[cos(y)/2] = √2
{tan[cos(y)/2]}^2 = 2
{sin[cos(y)/2]}^2 = 2{cos[cos(y)/2]}^2
1 - {cos[cos(y)/2]}^2 = 2{cos[cos(y)/2]}^2
3{cos[cos(y)/2]}^2 = 1
cos[cos(y)/2] = 1/√3
cos(y) = 2arccos(1/√3)