Question 18
Let $\alpha, \beta$, and $\gamma$ be three real numbers. Suppose that
$$
\begin{aligned}
\cos \alpha+\cos \beta+\cos \gamma & =1 \\
\sin \alpha+\sin \beta+\sin \gamma & =1
\end{aligned}
$$
Find the smallest possible value of $\cos \alpha$.
$$
\begin{aligned}
\cos \alpha+\cos \beta+\cos \gamma & =1 \\
\sin \alpha+\sin \beta+\sin \gamma & =1
\end{aligned}
$$
Find the smallest possible value of $\cos \alpha$.