I have the following problem. Let $X_1,...,X_n$ be a random sample of i.i.d random variables with density $$f_\theta=\begin{cases} \theta x +\frac{1}{2},&\text{if }-1\le x\le 1\\ 0 ,&\text{elsewhere} \end{cases}$$
Let $\hat\theta(X)=\frac{3\bar{X}}{2}$ an estimator of $\theta$.
I want to prove that $\hat\theta(X)$ is not sufficient by giving a specific example where $P(X=x|\hat\theta(X)=t)$ depends on $\theta$.
Any help would be appreciated.