$\theta_0=1$ in MA process

Question

Let $X_t$ be an MA$(q)$ process defined as \begin{equation} X_{t}=\mu +\overset{q}{\underset{j=0}{\sum }}\theta_{j}\varepsilon_{t-j}=\mu +\theta_{0}\varepsilon_{t}+\theta_{1}\varepsilon_{t-1}+\theta_{2}\varepsilon_{t-2} + \ldots \end{equation} where we ask that $\theta_0=1$. This requirement is for "identifiability purpose". What does the latter mean mathematically I cannot find any explicit and rigorous explanation of why we ask that $\theta_0=1$