<s>[INST] A circular disk of radius $1$ is used to represent a coin. The coin is carefully placed on a corner of a square table, and it is rolled with a constant speed, along a straight line which forms angle $\theta$ with a side of the square. When the coin reaches the opposite corner of the square, the center of the coin has traveled a distance $d$. We are given that $d = 1 + \pi$ and $\theta = 45^\circ$. Find the side length $s$ of the square.[/INST]