Let $X \in \text{Bernoulli}(\theta)$ be a D207: Bernoulli random boolean number.
A D5075: Random integer $R \in \text{Random} \{ -1, 1 \}$ is a rademacher random integer with parameter $\theta \in [0, 1]$ if and only if $$\begin{equation} R \overset{d}{=} 2 X - 1 \end{equation}$$