Type II error against a triangular density

Consider the problem of testing $H_{0}:X\sim f_{0}$ against $H_{1}:X\sim f_{1}$ based on a sample of size 1, where $$f_{0}(x)=\begin{cases}1,&0\le x\le 1\\0,&\text{otherwise}\end{cases}\quad\text{and}\quad f_{1}(x)=\begin{cases}2-2x,&0\le x\le 1\\0,&\text{otherwise}\end{cases}$$ Then, the probability of Type II error of the most powerful test of size $\alpha=0.1$ is equal to