(7) Let $y=\sin x+\cos x+\tan x+\cot x+\sec x+\csc x$, then the minimum value of $|y|$ is $\qquad$ .
(7) $2 \sqrt{2}-1$ Hint:
$$
y=\sin x+\cos x+\frac{1}{\sin x \cos x}+\frac{\sin x+\cos x}{\sin x \cos x} .
$$

Let $t=\sin x+\cos x$, then $\sin x \cos x=\frac{1}{2}\left(t^{2}-1\right)$, where $|t| \leqslant \sqrt{2}$, and $|t| \neq 1$.
$$
\begin{aligned}
y & =t+\frac{2}{t^{2}-1}+\frac{2 t}{t^{2}-1} \\
& =t+\frac{2}{t-1} \\
& =t-1+\frac{2}{t-1}+1 .
\end{aligned}
$$

When $t>1$,
$$
t-1+\frac{2}{t-1} \geqslant 2 \sqrt{2},
$$

at this time $y \geqslant 2 \sqrt{2}+1$;
When $t<1$,
$$
-y=1-t+\frac{2}{1-t}-1 \geqslant 2 \sqrt{2}-1 .
$$

Therefore, $|y| \geqslant 2 \sqrt{2}-1$, and the equality is achieved when $t=1-\sqrt{2}$. Thus, the minimum value of $|y|$ is $2 \sqrt{2}-1$.