The expression simplifies to twice the usual

Let $X_1,X_2,\dots ,X_n$ be a random sample from $N(\theta ,1)$ distribution, where $\theta \in \mathbb{R}$ is unknown. Let ${\delta }_n$ be the Bayes estimator of $\theta$, under the squared error loss function $L(\theta ,a)=(a-\theta {)}^2,a,\theta \in \mathbb{R}$ and the prior distribution N(1, 2). If $(1/\sqrt{n})[(2n+1){\delta }_n-1-2n\theta ]$ converges in distribution to a random variable Z, as $n\to \infty$, then which of the following statements are true?