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Geometry Level 3

Let \(N\) and \(M\) be two real numbers such that

\(N=\tan{20}+\tan{40}+\sqrt{3}\times \tan{20}\tan{40}\)

\(M=\cot{16}\cot{44}+\cot{44}\cot{76}-\cot{76}\cot{16} \)

Find the value of \(\dfrac M{N^2} \).

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