What is (1+\cot \theta-\text{cosec } \theta)(1+\tan \theta+\sec \theta) equal to?

Explanation

Substitute \theta = 45^\circ into the expression: (1 + 1 - \sqrt{2})(1 + 1 + \sqrt{2}) = (2 - \sqrt{2})(2 + \sqrt{2}) = 2^2 - (\sqrt{2})^2 = 4 - 2 = 2.

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