UMVUE of the reciprocal of an exponential rate

Let $X_1,…,X_n$ be a random sample from a population with probability density function

$$f_\theta(x)=\begin{cases}\theta e^{-\theta x}, & x>0,\ 0, & \text{otherwise,}\end{cases}$$

where $\theta>0$ is an unknown parameter. Then, the uniformly minimum variance unbiased estimator for $\frac1\theta$ is