11. Given $\frac{1}{\sin \theta}+\frac{1}{\cos \theta}=\frac{35}{12}, \theta \in\left(0, \frac{\pi}{2}\right)$. Find $\theta$.
Solve:
$$
\frac{\sin \theta+\cos \theta}{\sin \theta \cos \theta}=\frac{35}{12} \Rightarrow 12(\sin \theta+\cos \theta)=35 \sin \theta \cos \theta \text {. Let } t=\sin \theta+\cos \theta \text {, }
$$

then $12 t=\frac{35}{2}\left(t^{2}-1\right) \Rightarrow 35 t^{2}-24 t-35=(5 t-7)(7 t+5)=0 \Rightarrow t=\frac{7}{5}$ or $t=-\frac{5}{7}$ (discard).

So $\theta=\arcsin \frac{3}{5}$ or $\theta=\arcsin \frac{4}{5}$.