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