Because each side of an angle has asupplementaryangle, there are two exterior angles per vertex.
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Once again the product to sum identity has been applied and the second term has been rewritten in terms of itssupplementaryangle.
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The exterior angle is thesupplementaryangleto the interior angle.
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Being equivalent to the "square" of a sine, the spread of both an angle and itssupplementaryangleare equal.
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The product to sum identity has been applied twice and the middle two terms cancel out on account of being cosines of supplementary angles.
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