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.