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The $P_n$ and the $P_n$ are not the same :P$_n$ (In case someone really was confused: the former $P_n$ is a path graph, the latter one is a Legendre polynomial)
Augh! I actually had been thinking about this example, but I did the calculations wrong and I thought that $\Theta$ wasn't a spanning tree :( :( Thanks for your diligence!
