6. Let $\alpha, \beta, \gamma$ be the angles formed by the body diagonal of a rectangular parallelepiped with the three faces meeting at a vertex. Then
$$
f(\alpha, \beta, \gamma)=\sum \frac{\sin ^{4} \alpha+\sin ^{2} \beta}{\sin ^{2} \beta+\sin ^{2} \gamma}
$$

the range of values for $f(\alpha, \beta, \gamma)$ is $\qquad$ (where “$\sum$” denotes the cyclic sum).
6. $[2,+\infty)$.

From the problem, we have
$$
\begin{array}{l}
\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=1 . \\
\text { Then } \sum \frac{\sin ^{4} \alpha+\sin ^{2} \beta}{\sin ^{2} \beta+\sin ^{2} \gamma}+1 \\
=\sum\left(\frac{\sin ^{4} \alpha+\sin ^{2} \beta}{\sin ^{2} \beta+\sin ^{2} \gamma}+\sin ^{2} \alpha\right) \\
=\sum \frac{\sin ^{2} \alpha+\sin ^{2} \beta}{\sin ^{2} \beta+\sin ^{2} \gamma}
\end{array}
$$
$\geqslant 3$.
Thus, $f(\alpha, \beta, \gamma) \geqslant 2$.