Find the area of a spherical triangle made by the points $(0, 0, 1)$, $(0, 1, 0)$ and $(\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}})$. 
Calculate the area of the spherical triangle defined by the points $(0, 0, 1)$, $(0, 1, 0)$ and $(\dfrac{1}{\sqrt{2}}, 0, \dfrac{1}{\sqrt{2}})$.

I have come up with this:
From the spherical Gauss-Bonnet Formula, where $T$ is a triangle with interior angles $\alpha, \beta, \gamma$. Then the area of the triangle $T$ is $\alpha + \beta + \gamma - \pi$.
How do I work out the interior angles in order to use this formula?
Any help appreciated.

See Mathcad implementation of equation for finding area when three co-ordinates given for sphere centered at (0,0,0)
See the paper "On the Measure of Solid Angles" by Folke Eriksson.
