# Expectation of product of normal CDFs

Suppose $$X \sim N(0, I)$$. How would I go about calculating \begin{align*} \mathbb{E}[\Phi(\Delta_1 + \theta_1^\intercal X)\Phi(\Delta_2 + \theta_2^\intercal X)]? \end{align*} where $$\Delta_1, \Delta_2 \in \mathbb{R}, \theta_1, \theta_2 \in \mathbb{R}^p$$. Here, $$\Phi(x) = (2\pi)^{-1/2}\int_{-\infty}^{x}\exp(-t^2/2)dt$$ is the standard normal CDF. I've found previous posts for which only one $$\Phi$$ was present, but not both, and the strategy from one doesn't follow with two now.