Michael's trigonometric expression

Algebra Level 3

Find the smallest positive integer \(x\) such that \[\tan{x^{\circ}}=\dfrac{\cos{2013^{\circ}}+\sin{2013^{\circ}}}{\cos{2013^{\circ}}-\sin{2013^{\circ}}}.\]

This problem is shared by Michael T. from AIME.

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