Simple trig shows that

tan(OAD) = tan(40°)*tan(30°)*tan(20°)

and any scietific calculator will show that angle OAD = 10° to
the accuracy of the calculator.

However, the standard formula for

tan(3*x) = (3*tan(x) - (tan(x)^{3}))/(1-3*(tan(x))^{3})

Let t = tan(x) and T = tan(3*x) then

t^{3}-3*T*t^{2} - 3*t + T = 0

If x = 10° then this is a cubic equation whose roots are tan(10°)
, tan(130°) and tan(250°).

Minus the product of these will be the constant
term T = tan(30°).

That is -tan(30°) = tan(10°) * tan(130°)* tan(250°)

But tan(130°) = -tan(50°) and tan(250°) = tan(70°)
from which the result follows.

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