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)