\textbf{113.} What is the solution set of the trigonometric equation $\sin^2 x + \cos^2 x = 1 - \dfrac{1}{2}\sin 2x$ on the interval $[0, 2\pi]$?
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(1) $\dfrac{5\pi}{2}$ \qquad
(2) $\dfrac{7\pi}{2}$ \qquad
(3) $2\pi$ \qquad
(4) $3\pi$
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