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tan2(theta) + 5*tan(theta) = 0 => tan(theta)*[tan(theta) + 5] = 0=> tan(theta) = 0 or tan(theta) = -5If tan(theta) = 0 then tan(theta) + cot(theta) is not defined.If tan(theta) = -5 then tan(theta) + cot(theta) = -5 - 1/5 = -5.2
It is cotangent(theta).
Cosine squared theta = 1 + Sine squared theta
It is -sqrt(1 + cot^2 theta)
The letter after Theta is Iota.