\(\Leftrightarrow2\sqrt{2}sinx.cosx-\sqrt{6}\left(1-2sin^2x\right)-2\left(\sqrt{3}-\sqrt{2}\right)sinx-2cosx+\sqrt{6}-2=0\)
\(\Leftrightarrow2cosx\left(\sqrt{2}sinx-1\right)+2\left(\sqrt{6}sin^2x-\left(\sqrt{3}-\sqrt{2}\right)sinx-1\right)=0\)
\(\Leftrightarrow cosx\left(\sqrt{2}sinx-1\right)+\left(\sqrt{2}sinx-1\right)\left(\sqrt{3}sinx+1\right)=0\)
\(\Leftrightarrow\left(\sqrt{2}sinx-1\right)\left(cosx+\sqrt{3}sinx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=\dfrac{\sqrt{2}}{2}\\\dfrac{\sqrt{3}}{2}sinx+\dfrac{1}{2}cosx=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow...\)
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