A PDF of a random variable $X$ is $$f(x|\theta)=max({0,1-|x-\theta|})$$ Real number $\theta$ is a unknown parameter. I consider the hypothesis testing of a level of $$\alpha(0\lt\alpha\leq0.05)\\\ H_0:\theta=0 \\\ H_1:\theta\neq0$$ We reject the $H_0$ when it is found to be $|X|\gt c$.
What is a value of $c$?
I set $$P(|max({0,1-|x-\theta|}|)>c|\theta=0)=\alpha \\\ P((|max{0,1-|x|}|)>c)=\alpha$$
but could not move on from here. Can anyone help me?