The spherical distance between two points $P\_1=(0,0,1)$ and $P\_2=(\frac{1}{2\sqrt{2}},\frac{1}{2\sqrt{2}},{-}\frac{\sqrt{3}}{2})$ is $\frac{5\pi }{6}$. 

I am at a loss as to how the spherical distance was obtained. My notes just give the answer but no step by step derivation. Any help would be much appreciated.