The value of $\arctan(1)$ is:
$$ \arctan(1) = \frac{\pi}{4} $$
This is because the tangent of $\frac{\pi}{4}$ is 1, and $\frac{\pi}{4}$ lies in the first quadrant where the arctangent function is defined (i.e., between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$).
So, the final answer is:
$$ \boxed{\frac{\pi}{4}} $$