2. In $\triangle A B C$, the sides opposite to $\angle A, \angle B, \angle C$ are $a, b, c$ respectively. If $a^{2}+b^{2}=t c^{2}$, and $\cot C=$ $2004(\cot A+\cot B)$, then the value of the constant $t$ is $\qquad$
$2.4009$