Confidence coefficient of an interval based on $X/\theta$

Let $X$ be a random sample of size $1$ from the probability density function

$$f(x\mid\theta)=\begin{cases}\dfrac3{\theta^3}(\theta-x)^2,&0<x<\theta,\\0,&\text{otherwise.}\end{cases}$$

If $\left(\dfrac X{1-\lambda_1},\dfrac X{1-\lambda_2}\right)$ is a confidence interval for $\theta$ with confidence coefficient $1-\alpha$, where $\lambda_i\in(0,1)$, $i=1,2$, $\lambda_1<\lambda_2$, and $\alpha\in(0,1)$, then which of the following statements is true?