Mixmatch

Algebra Level 1

If \(\color{blue}{a},\color{red}{b},\) and \(\color{green}{c}\) are distinct reals such that \[\color{blue}{a}+\dfrac {1}{\color{red}{b}}=\color{red}{b}+\dfrac {1}{\color{green}{c}}=\color{green}{c}+\dfrac {1}{\color{blue}{a}},\] then find the value of \(|\color{blue}{a}\color{red}{b}\color{green}{c}|.\)