Method of moments for Laplace-normal mixture

Let $2.5, -1.0, 0.5, 1.5$ be the observed values of a random sample of size $4$ from a continuous distribution with the probability density function $$f(x)=\frac{1}{8}e^{-|x-2|} + \frac{3}{4\sqrt{2\pi}} e^{-\frac{1}{2}(x-\theta)^2},\quad x\in\mathbb{R},$$ where $\theta\in\mathbb{R}$ is unknown. Then the method of moments estimate of $\theta$ equals __________ (round off to $2$ decimal places)