삼각방정식 실근의 합

$( \sin x - \cos x ) ( 4 \sin ^{2} x + 4 \sin x \cos x + 4 \cos ^{2} x - 3 ) = 0$ $\displaystyle \sqrt{2} \sin \left( x - \frac{\pi}{4} \right) ( 2 \sin 2 x + 1 ) = 0$ $\displaystyle \sin \left( x - \frac{\pi}{4} \right) = 0$ 또는 $\displaystyle \sin 2 x = - \frac{1}{2}$ $\displaystyle x = n \pi + \frac{\pi}{4}$ 또는 $\displaystyle x = \frac{n \pi}{2} + ( - 1 ) ^{n} \frac{7}{12} \pi$ 따라서 $0 \leq x \leq \pi$ 이므로, 해는 $\displaystyle \frac{\pi}{4}$, $\displaystyle \frac{7}{12} \pi$, $\displaystyle \frac{11}{12} \pi$