All three are similar:
1) $-\log\theta$ is monotonically decreasing on $(0;1]$ from $+\infty$ to $0$, therefore, for $y\ge 0$: $F_{-\log\theta}(y)=Pr\{-\log\theta<y\}=Pr\{\theta>e^{-y}\}=1-e^{-y}$, and density is $e^{-y}$.
2) $\theta(1-\theta)$ is increasing on $[0;1/2]$ from $0$ to $1/4$, and decreasing on $[1/2;1]$ from $1/4$ to $0$, therefore, for $y\in[0;1/4]$: $F_{\theta(1-\theta)}(y)=Pr\{\theta(1-\theta)<y\}=1-Pr\{\theta(1-\theta)>y\}=1-Pr\{\theta^2-\theta+y<0\}=1-\sqrt{1-4y}$, and density is just the derivative.
3) Similarly. I am pretty sure you can now get it done by yourself.