1. **Problem statement:** Find all values of $\theta$ such that $\tan \theta = 2$. 2. **Formula and rules:** The tangent function is periodic with period $\pi$, meaning if $\tan \theta = 2$, then all solutions are given by: $$\theta = \arctan(2) + k\pi, \quad k \in \mathbb{Z}$$ 3. **Find the principal value:** Calculate the principal value $\theta_0 = \arctan(2)$. 4. **General solution:** Since tangent repeats every $\pi$, the other values are: $$\theta = \theta_0 + k\pi, \quad k = 0, \pm 1, \pm 2, \ldots$$ 5. **Explanation:** This means if you find one angle where tangent is 2, adding or subtracting multiples of $\pi$ will give all other angles with the same tangent value. **Final answer:** $$\boxed{\theta = \arctan(2) + k\pi, \quad k \in \mathbb{Z}}$$