MLE at the boundary of a $\theta$-dependent support

Suppose $x_1=-2$, $x_2=1$, $x_3=3$, $x_4=-4$ are observed values of a random sample from the density

$$f(x,\theta)=\frac{e^{-x}}{e^{\theta}-e^{-\theta}}, \qquad -\theta<x<\theta,\quad \theta>0 .$$

Then the maximum likelihood estimator of $\theta$ is: