If the equation ${\cot }^{4}x-2\cos e{c}^{2}x+a^2=0$  has at least one solution then, sum of all possible integral values of ‘a’ is equal to

$Wehave{\cot }^{4}x-2\cos e{c}^{2}x+a^2=0$

$\Rightarrow {\cot }^{4}x-2\left(1+{\cot }^{2}x\right)+a^2=0$

$\Rightarrow {\cot }^{4}x-2{\cot }^{2}x+a^2-2=0$

$\Rightarrow {\left({\cot }^{2}x-1\right)}^2=3-a^2$

To have at least one solution $3-a^2\ge 0$

$\Rightarrow a^2-3\le 0$

$a\in \left[-\sqrt{3},\sqrt{3}\right]$

$\Rightarrow a=-1,0,1$

$\therefore$sum of all values of ‘a’ = 0