how do you simplify tan theta plus cot theta using fundamental identities

Theta is a Greek letter. Here is all of the ones I know:

α β γ ε η θ ω π ξ

$$tan\theta+cot\theta\\\\ =\frac{sin\theta}{cos\theta}+\frac{cos\theta}{sin\theta}\\\\ =\frac{sin^2\theta}{cos\theta sin\theta}+\frac{cos^2\theta}{sin\theta\cos\theta}\\\\ =\frac{1}{cos\theta sin\theta}\\\\ =\frac{2}{2cos\theta sin\theta}\\\\ =\frac{2}{sin2\theta}\\\\$$

You can try this:  tan(θ) + cot(θ)  

   =  tan(θ)  +  1/tan(θ)  

   =  tan²(θ)/tan(θ)  +  1/tan(θ)

   =  [tan²(θ) + 1] / tan(θ)  

   =   sec²(θ)/tan(θ)

or this:   tan(θ) + cot(θ)

=  sin(θ)/cos(θ)  +  cos(θ)/sin(θ)

=  [sin(θ)sin(θ)]/[sin(θ)cos(θ)]  +  [cos(θ)cos(θ)]/[sin(θ)cos(θ)]

=  sin²(θ)/[sin(θ)cos(θ)]  +  cos²(θ)/[sin(θ)cos(θ)]

=  [sin²(θ) + cos²(θ)]/[sin(θ)cos(θ)]

=  1/[sin(θ)cos(θ)]