<s>[INST] $8\sin x\cos x-\sqrt{6} \sin x- \sqrt{6} \cos x+1=0$, Solve for $x$ 
Solve for $x:0\leq x \leq \frac{\pi}{2}$
$$8\sin x\cos x-\sqrt{6} \sin x- \sqrt{6} \cos x+1=0$$

My attempt,
I changed it into $$1+4 \sin 2x-2\sqrt{3} \sin (x+\frac{\pi}{4})=0$$
 [/INST] Let $\sin{x}+\cos{x}=t$ and we get a quadratic equation:
$$4(t^2-1)-\sqrt6t+1=0.$$
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