My 100 followers problem!

Algebra Level 3

If \(a+b+c=1\) and \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3\), where \(a\), \(b\) and \(c\) are non-zero reals, then find \((a+b)ab+(b+c)bc+(c+a)ca\).

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