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http://amc.maa.org/a-activities/a7-problems/putnam/-pdf/2011.pdf

The solution is here but it starts off by claiming that (-1, 2/π) works and then they show it works.

http://amc.maa.org/a-activities/a7-problems/putnam/-pdf/2011s.pdf

My question is how they found (-1, 2/π)