3. Given $n(n \in \mathbf{N}, n \geqslant 2)$ is a constant, and $x_{1}$, $x_{2}, \cdots, x_{n}$ are any real numbers in the interval $\left[0, \frac{\pi}{2}\right]$. Then the function
$$
\begin{array}{l}
f\left(x_{1}, x_{2}, \cdots, x_{n}\right) \\
=\sin x_{1} \cdot \cos x_{2}+\sin x_{2} \cdot \cos x_{3}+\cdots+ \\
\quad \sin x_{n} \cdot \cos x_{1}
\end{array}
$$

has a maximum value of $\qquad$
3. $\frac{n}{2}$