6. Let $\alpha, \beta, \gamma \in \mathbf{R}$, and satisfy $\sin \alpha \cos \beta+|\cos \alpha \sin \beta|=\sin \alpha|\cos \alpha|+|\sin \beta| \cos \beta$. Then the minimum value of $(\tan \gamma-\sin \alpha)^{2}+(\cot \gamma-\cos \beta)^{2}$ is $\qquad$.
6. 3-2 $\sqrt{2}$ Detailed Explanation: Given the equation factorizes to $(\sin \alpha-|\sin \beta|)(\cos \beta-|\cos \alpha|)=0$. Let $x=\sin \alpha, y=$ $\cos \beta$. Then $\left(x-\sqrt{1-y^{2}}\right)\left(y-\sqrt{1-x^{2}}\right)=0$. Thus, $x=\sqrt{1-y^{2}}$ or $y=\sqrt{1-x^{2}}$. Also, the point $(\tan \gamma, \cot \gamma)$ lies on the hyperbola $x y=1$, so the required value is the square of the minimum distance between the two graphs. It is easy to see from the graph that $3-2 \sqrt{2}$ is the desired result.