3. Given that the inverse function of $y=f(x)$ is $g(x)=\log _{\sin ^{2} \theta}\left(\frac{1}{x}-\cos ^{2} \theta\right)\left(\right.$ constant $\left.\theta \in\left(0, \frac{\pi}{2}\right)\right)$. Then the solution set of the equation $f(x)=1$ is $\qquad$ .
3. $\{1\}$.

The required is $g(1)=\log _{\sin ^{2} \theta}\left(\frac{1}{1}-\cos ^{2} \theta\right)=1$.