The value of $$(1 + \cot \theta - \cosec \theta )(1 + \cos \theta + \sin \theta)\sec \theta = ?$$

$$(1 + \cot \theta - \cosec \theta )(1 + \cos \theta + \sin \theta)\sec \theta$$
Let $$\theta = 45\degree$$,
$$(1 + \cot 45\degree - \cosec 45\degree )(1 + \cos 45\degree + \sin 45\degree)\sec 45\degree$$
= $$(1 + 1 - \sqrt{2})(1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})\sqrt{2}$$
= $$(2 - \sqrt{2})(\frac{2 + \sqrt{2}}{\sqrt{2}})\sqrt{2}$$
= $$(2 - \sqrt{2})(2 + \sqrt{2})$$
= $$(2^2 - (\sqrt{2})^2)$$ = 4 - 2 = 2