Mind your C's and D's

\[ \begin{array} {c c c } & & \color{green}{C} \\ + & \color{green}{C} & \color{green}{C} \\
\hline & \color{purple}{D} & 4 \\ \end{array} \]

In the above cryptogram, \(\color{green}{C}\) and \(\color{purple}{D}\) represent distinct digits. What is the value of \( \color{green}{C} \)?

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