What is the general solution for tan^3(θ)+tan^2(θ)-3tan(θ)-3=0 ?

The general solution for tan^3(θ)+tan^2(θ)-3tan(θ)-3=0 is θ=(3pi)/4+pin,θ=(2pi)/3+pin,θ= pi/3+pin

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tan^3(θ)+tan^2(θ)-3tan(θ)-3=0

tan^{3} (θ) + tan^{2} (θ) - 3 tan (θ) - 3 = 0

θ = \frac{3 π}{4} + πn, θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

Solution steps

tan^{3} (θ) + tan^{2} (θ) - 3 tan (θ) - 3 = 0

Solve by substitution

tan (θ) = - 1, tan (θ) = - 3, tan (θ) = 3

tan (θ) = - 1 : θ = \frac{3 π}{4} + πn

tan (θ) = - 3 : θ = \frac{2 π}{3} + πn

tan (θ) = 3 : θ = \frac{π}{3} + πn

Combine all the solutions

θ = \frac{3 π}{4} + πn, θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

x, sec (x) tan (x) = 0

csc (x) = \frac{1}{4}

3 sin (x) + 2 cos (x) = 1

tan (\frac{x}{2}) \cdot tan (x) = - 3

x, sin (x) cos (x) = 1

What is the general solution for tan^3(θ)+tan^2(θ)-3tan(θ)-3=0 ?
The general solution for tan^3(θ)+tan^2(θ)-3tan(θ)-3=0 is θ=(3pi)/4+pin,θ=(2pi)/3+pin,θ= pi/3+pin