In the age hardening process for Al-4.5 wt% Cu alloy, the sequence of precipitation occurs as the alloy is aged at room temperature. The correct order of precipitation stages is as follows:
1. GP zone: The initial stage where clusters of solute atoms form, called the Guinier-Preston (GP) zones. These zones are not yet distinct precipitates, but the atomic clusters have some short-range ordering.
2. \( \theta'' \): The GP zones evolve into the \( \theta'' \) phase, which is a more ordered precipitate.
3. \( \theta' \): As the aging continues, the \( \theta'' \) phase transforms into the \( \theta' \) phase, which is more stable and larger in size.
4. \( \theta \): Finally, the \( \theta' \) phase coarsens and forms the stable \( \theta \) phase, which is a solid solution of copper in aluminum.
Thus, the correct sequence of precipitation is:
\[
{GP zone} \rightarrow \theta'' \rightarrow \theta' \rightarrow \theta
\]
Therefore, the correct answer is option (A).