Statistical Inference — critical value of a fixed-size normal mean test

Let $(X_1, X_2, X_3, …, X_n)$ be a random sample of size $n$ from a normal distribution $N(\mu, 1)$. $w_0 = \{(x_1, x_2, x_3, …, x_n) ; \bar{X} > \theta\}$ is critical region of size $\alpha$ for testing $H_0 : \mu = 0$ against $H_1 : \mu = 4$. What is the value of $\theta$?