Let \(a_{}^{}, b_{}^{}, c_{}^{}\) be the three sides of a triangle, and let \(\alpha_{}^{}, \beta_{}^{}, \gamma_{}^{}\), be the angles opposite them. If \(a^2+b^2=1989^{}_{}c^2\), find $$\frac{\cot \gamma}{\cot \alpha+\cot \beta}$$

(第七届AIME1989 第10题)