15.1.13 Theory of random processes

Problem: The random process \( X(t), t \geq 0 \), is defined by the formula \( X(t)=\alpha \cos (t+\beta)+\varepsilon \), where \( \alpha, \beta, \varepsilon \) are independent random variables, moreover \( \alpha \sim N(0,1), \varepsilon \sim N\left(0, \sigma^{2}\right), \beta \sim U[-\pi, \pi] \). Is the process \( X(t), t \geq 0 \) stationary in broad sense?