If $a\bigg(\large\frac{1}{b}+\frac{1}{c}\bigg)$$,\:b\bigg(\large\frac{1}{c}+\frac{1}{a}\bigg)$$,\:c\bigg(\large\frac{1}{a}+\frac{1}{b}\bigg)$ are in A.P., then prove that $a,b,c$ are in A.P.

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