My 100 followers problem!

Algebra Level 3

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

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