Area of a Spherical Triangle from Side Lengths I am currently working on a proof involving finding bounds for the f-vector of a simplicial $3$-complex given an $n$-element point set in $\mathbb{E}^3$, and (for a reason I won't explain) am needing to find the answer to the following embarrassingly easy (I think) question.

What is the area of a spherical triangle with all equal side lengths equal to $\pi / 3$?

I have tried using L'Juilier's Theorem, but the first term $$\tan(\frac{1}{2}s)=\tan(\frac{1}{2}(\frac{3\pi}{3}))=\tan(\frac{\pi}{2})$$
is undefined, where $s$ is the semiperimeter (perimeter divided by 2).
Any ideas for how to compute this?

As an equilateral spherical triangle gets arbitrarily small, its angles all approach π/3. So one might say there is a degenerate spherical triangle whose angles are in fact all π/3 and whose area is 0.
