What is the value of ( 1+ tanθ - secθ) ( 1 + cot θ+ cosec θ) ?

( 1 + tanθ - secθ) ( 1 + cot θ+ cosec θ)

Put θ = 45°

(1 + tan45 - sec45)(1 + cot45 + cosec45)

= (1 + 1 - $\sqrt{2}$)(1 + 1 + $\sqrt{2}$)

= (2 + $\sqrt{2}$)(2 + $\sqrt{2}$)

= (4 - ($\sqrt{2}$)²)    [(a+b)(a-b) = a²-b²}

= 2