2. Find the range of real number $a$ such that for any real number $x$ and any $\theta \in\left[0, \frac{\pi}{2}\right]$, we have
$$
\begin{array}{l}
(x+3+2 \sin \theta \cdot \cos \theta)^{2}+(x+u \sin \theta+u \cos \theta)^{2} \\
\geqslant \frac{1}{8} .
\end{array}
$$
$\left(a \leqslant \sqrt{6}\right.$ or $\left.a \geqslant \frac{7}{2}\right)$