tan(180/7)^2+tan(360/7)^2+tan(540/7)^2(cot(180/7)^2+cot(360/7)^2+cot(540/7)^2)

tan(180/7)^2+tan(360/7)^2+tan(540/7)^2(cot(180/7)^2+cot(360/7)^2+cot(540/7)^2)
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ANSWER: 97.7826 approx., tan(180/7)=0.48157 approx; tan(360/7)=1.25396 approx; tan(540/7)=4.38129 approx.

Let A=180/7: (tanA)^2+(tan2A)^2+(tan3A)^2(1/(tanA)^2+1/(tan2A)^2+1/(tan3A)^2).

Let B=(tanA)^2+(tan2A)^2, then B+((tan3A)^2)B/(tanAtan2A)^2+1 is the expression=1+B(1+(tan3A/tanAtan2A)^2)

B can be evaluated: 1.80433 approx.

Let C=(tan3A/tanAtan2A)^2=52.6391 approx.

The expression becomes 1+B(1+C)=1+1.80433*53.6391=97.7826 approx.

 

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