Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π) :
tan θ + cot θ = 4 sin 2θ

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Hmm...
\[tan θ + cot θ\]\[= \frac{sinθ}{cosθ}+\frac{cosθ}{sinθ} =...?\]

after that: \[\frac{ 1 }{ \cos \theta \sin \theta} =4\sin2\theta \]

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