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in a triangle angle A+B+C=180
so,let us assume that ∠A=∠B=∠C=60
now,Tan A + Tan B + Tan C ≥ Tan 60+Tan 60 +Tan 60
Tan A + Tan B + Tan C ≥ √3+√3+√3
Tan A + Tan B + Tan C ≥ 3√3
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