Three points are located on the surface of the ellipsoid: 2x2 + 2y2 + z2 = 3. One has a x coordinate of 0, another has a y coordinate of 0, and the last has a z coordinate of 0.
What is the largest possible equilateral triangle (in terms of area) that can be made using these three points as the corners? How many distinct equilateral triangles of this size are possible?
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