Individually divisible?

I have chosen four integers \({\color{red}a}, {\color{blue}b}, {\color{green}c},\) and \({\color{purple}d}\) so that all five of the following sums are values divisible by 3:

  • \({\color{red}a}+{\color{blue}b}+{\color{green}c}\)
  • \({\color{red}a}+{\color{blue}b}+{\color{purple}d}\)
  • \({\color{red}a}+{\color{green}c}+{\color{purple}d}\)
  • \({\color{blue}b}+{\color{green}c}+{\color{purple}d}\)
  • \({\color{red}a} + {\color{black}0}+{\color{black}0}. \)

Are \({\color{blue}b},\) \({\color{green}c},\) and \({\color{purple}d}\) also guaranteed to be divisible by 3?

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