Choose the correct option. Justify your choice.

(1 + tan θ + sec θ)(1 + cot θ - cosec θ) =

1. 0

2. 1

3. 2

4. -1

Solving,

$\Rightarrow \text{(1 + tan θ + sec θ)(1 + cot θ - cosec θ)} \\[1em] \Rightarrow \Big(1 + \dfrac{\text{sin θ}}{\text{cos θ}} + \dfrac{1}{\text{cos θ}}\Big)\Big(1 + \dfrac{\text{cos θ}}{\text{sin θ}} - \dfrac{1}{\text{sin θ}}\Big) \\[1em] \Rightarrow \Big(\dfrac{\text{sin θ + cos θ + 1}}{\text{cos θ}}\Big)\Big(\dfrac{\text{sin θ + cos θ - 1}}{\text{sin θ}}\Big) \\[1em] \Rightarrow \dfrac{\text{(sin θ + cos θ)}^2 - 1^2}{\text{sin θ. cos θ}} \\[1em] \Rightarrow \dfrac{\text{sin}^2 θ + \text{cos}^2 θ + \text{2 sin θ. cos θ - 1}}{\text{sin θ. cos θ}} \\[1em] \Rightarrow \dfrac{1 + \text{2 sin θ.cos θ - 1}}{\text{sin θ. cos θ}} \\[1em] \Rightarrow \dfrac{\text{2 sin θ. cos θ}}{\text{sin θ.cos θ}} \\[1em] \Rightarrow 2.$

Hence, Option 3 is the correct option.