3. For $0 \leqslant \theta \leqslant \frac{\pi}{2}$, such that
$$
\cos ^{2} \theta+2 m \sin \theta-2 m-2<0
$$

always holds, the range of real number $m$ is $\qquad$
3. $m>\frac{1}{2}$.

When $\theta=\frac{\pi}{2}$, the inequality always holds.
When $\theta \in\left[0, \frac{\pi}{2}\right)$,
the original inequality
$$
\begin{aligned}
\Leftrightarrow m & >\frac{1}{2}(\sin \theta-1)+\frac{1}{\sin \theta-1}+1 \\
(\sin \theta & -1 \in[-1,0)) .
\end{aligned}
$$

When $\sin \theta-1=-1$, i.e., $\theta=0$, $\frac{1}{2}(\sin \theta-1)+\frac{1}{\sin \theta-1}$ has a maximum value of $-\frac{3}{2}$. Therefore, $m>\frac{1}{2}$.