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The value of the expression $$\cosec(85^\circ + \theta) - \sec(5^\circ - \theta) - \tan(55^\circ + \theta) + \cot(35^\circ - \theta)$$ is:
$$\cosec(85^\circ + \theta) - \sec(5^\circ - \theta) - \tan(55^\circ + \theta) + \cot(35^\circ - \theta)$$
= $$\cosec(85^\circ + \theta) - \sec(90 - (85^\circ + \theta)) - \tan(55^\circ + \theta) + \cot(90 - (55^\circ + \theta))$$
= $$\cosec(85^\circ + \theta) - \cosec(85^\circ + \theta) - \tan(55^\circ + \theta) + \tan(55^\circ + \theta) $$
= 0
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