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Does there exist an angle

Source: Baltic Way 2008, Problem 3

November 23, 2008
trigonometryalgebrapolynomialarithmetic sequencenumber theoryrelatively primealgebra unsolved

Problem Statement

Does there exist an angle α∈(0,π/2) \alpha\in(0,\pi/2) such that sin⁡α \sin\alpha, cos⁡α \cos\alpha, tan⁡α \tan\alpha and cot⁡α \cot\alpha, taken in some order, are consecutive terms of an arithmetic progression?
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