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HMMT Team 2019/3: Trig ineq with one degree of freedom

Source:

February 17, 2019
HMMTtrigonometryalgebra

Problem Statement

For any angle 0<θ<π/20 < \theta < \pi/2, show that 0<sin⁡θ+cos⁡θ+tan⁡θ+cot⁡θ−sec⁡θ−csc⁡θ<1.0 < \sin \theta + \cos \theta + \tan \theta + \cot \theta - \sec \theta - \csc \theta < 1.
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