1.

( 1 + \operatorname { cot } \theta + \operatorname { tan } \theta ) ( \operatorname { sin } \theta - \operatorname { cos } \theta ) = \frac { \operatorname { sec } \theta } { \operatorname { cosec } ^ { 2 } \theta } - \frac { \operatorname { cosec } \theta } { \operatorname { sec } ^ { 2 } \theta }

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