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Which one of the following is not a solution to the equation $\text{sin x}+\sqrt{2}=\text{-sin x}$ ?

$\cfrac{5\pi}{4}$

$\cfrac{7\pi}{4}$

$\cfrac{13\pi}{4}$

$-\cfrac{\pi}{4}$

$\cfrac{3\pi}{4}$