If the equation cot4⁡x−2cosec2⁡x+a2=0 has at least one  solution, then the sum of all possible integral values of a is equal to

cot4⁡x−21+cot2⁡x+a2=0 or  cot4⁡x−2cot2⁡x+a2−2=0 or  cot2⁡x−12=3−a2To have at least one solution 3−a2≥0a2−3≤0a∈[−3,3]Integral values are -1, 0, 1; therefore, the sum is 0.