We evaluate the infinite series for arctan(sqrt(3)/(3n^2 + 3n + 1)).

00:00 Lemma: arctan identity
00:56 Applying the identity
03:47 Cancellation
06:34 Evaluating the series
08:33 Counterexample
09:22 Known results
10:42 Proving the identity
13:26 Sufficient conditions
16:14 Checking the conditions hold