16 Jul '04 16:30>
Originally posted by observantUno...your steps do not give the same value. It is different from the value as calculated on the lines suggested by the poser .
There is perhaps another simpler way. Acolyte has worked out the angle between two adjacent faces of a regular tetrahedron is
cos^-1(1/3).
In a unit sphere,with center at O, let AOB be a vertical diameter. Now draw two planespassing through this diameter, and inclined at angle cosine inverse of 1/3, cut the sphere surface in the semi-great-circles AP ...[text shortened]... pi/cos^-1(1/3)) = 2 cos^-1(1/3).
I hope this gives the same value for W8 as from your relation.