If i have a random walk with $x(i+1)=x(i)+\cos(\theta_i)$ starting at $x(0)=0$ where $\theta_i \sim U[0,2\pi]$, then what would the distribution of my first passage time be? Specifically if I have $x(t)=Z $ what is the distribution of this $t$ for a fixed $Z\in \mathbb{R}$?
Any help would be appreciated.