Given ABC is a triangle, so ∠ A + ∠ B + ∠ C = 180°

Now applying tan on both sides

tan (A+B +C) = tan (180°)

tan (A + B + C) = 0 ----- (1)

Also given tan A + tan B + tan C = 0 ------ (2)

As per the formula of tan (A+B+C)

Now,

[from equation (1) ]

[from equation (2) ]

By cross multiplying

-tan A tan B tan C = 0

tan A tan B tan C = 0

therefore

Hence cot A cot B cot C = 0

The answer is option D.