6) If $\tan x_{1} \cdot \tan x_{2} \cdots \cdots \cdot \tan x_{2012}=1$, then the maximum value of $\sin x_{1} \cdot \sin x_{2} \cdot \cdots$ ・ $\sin x_{2012}$ is $\qquad$ .
6. $\frac{1}{2^{1006}}$ Hint: From $\tan x_{1} \cdot \tan x_{2} \cdots \cdot \tan x_{2012}=1$ we get
$$
\sin x_{1} \cdot \sin x_{2} \cdots \cdots \cdot \sin x_{2012}=\cos x_{1} \cdot \cos x_{2} \cdots \cdots \cdot \cos x_{2012} \text {, }
$$

Thus,
$$
\begin{aligned}
& 2^{2012}\left(\sin x_{1} \cdot \sin x_{2} \cdot \cdots \cdot \sin x_{2012}\right)^{2} \\
= & \sin 2 x_{1} \cdot \sin 2 x_{2} \cdots \cdots \cdot \sin 2 x_{2012} \leqslant 1 .
\end{aligned}
$$

Therefore,
$$
\sin x_{1} \cdot \sin x_{2} \cdots \cdot \sin x_{2012} \leqslant \frac{1}{2^{1006}},
$$

Equality holds when $x_{1}=x_{2}=\cdots=x_{2012}=\frac{\pi}{4}$. 
Hence, the maximum value of $\sin x_{1} \cdot \sin x_{2} \cdots \cdot \sin x_{2012}$ is $\frac{1}{2^{1006}}$.