$\Rightarrow \dfrac{1-\cos 2x}{2}+\dfrac{1-\cos 4x}{2}+\dfrac{1-\cos 6x}{2}+\dfrac{1-\cos 8x}{2}=2$
$\Rightarrow \cos 2x+\cos4x+\cos6x+\cos 8x=0 $
$\Rightarrow 2\cos 3x\cos x+2\cos 7x\cos x=0$
$\Rightarrow \cos x(\cos 3x+\cos 7x)=0$
$\Rightarrow 2\cos x\cos 5x\cos 2x=0$
$\Rightarrow \left[ \begin{array}{l} \cos x=0 \\ \cos 2x=0\\\cos 5x=0\end{array} \right .\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{2}+k\pi \\ 2x=\dfrac{\pi}{2}+k\pi \\3x=\dfrac{\pi}{2}+k\pi \end{array} \right .$
$\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{2}+k\pi \\ x=\dfrac{\pi}{4}+k\dfrac{\pi}{2} \\x=\dfrac{\pi}{6}+k\dfrac{\pi}{3} \end{array} \right .(k\in\mathbb Z)$
