The general value of ‘x’ satisfying the equation $2{\cot }^{2}x+2\sqrt{3}\cot x+4\cos ecx+8=0$ is (where $n\in I$)

$({\cot }^{2}x+2\sqrt{3}\cot x+3)+({\cot }^{2}x+1)+(4\cos ecx+4)=0$

${(\cot x+\sqrt{3})}^2+{(\cos ecx+2)}^2=0$

$\Rightarrow \cot x=-\sqrt{3}and\cos ecx=-2$

General solution is $2n\pi -\frac{\pi }{6}$