1. The problem states that $\sin\theta = \sin\alpha$. 2. Using the sine function properties, if $\sin A = \sin B$, then $A = B + 2k\pi$ or $A = \pi - B + 2k\pi$, where $k$ is any integer. 3. Therefore, the general solutions for $\theta$ are: $$\theta = \alpha + 2k\pi$$ or $$\theta = \pi - \alpha + 2k\pi$$ where $k \in \mathbb{Z}$. 4. This means $\theta$ can be equal to $\alpha$ plus any full rotation $2k\pi$, or it can be the supplementary angle to $\alpha$ plus any full rotation $2k\pi$.