By Kaarel Hänni.
Initially, four birds, labeled A, B, C, and D, are positioned at the vertices of a regular tetrahedron with side length a. At time t=0, all birds begin flying. For all t>0, each bird flies directly toward another bird in the following pattern: A flies toward B, B flies toward C, C flies toward D, and D flies toward A. For any t>0, the speeds of all the birds are equal.
Calculate the total distance traveled by bird A from the start until all birds meet at a single point.
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