A circuit is built by connecting wires in a pattern of triangles, as shown above. Point is the common vertex of all triangles, and point is a vertex of one of the triangles at the end of the pattern.
Let be the number of triangles in the pattern. (In the diagram above, .)
Determine the resistance between points and in the limit where the pattern of wires grows to infinitely many triangles, i.e.
Give your answer to 3 decimal places.