Let the set of all a ∈ R such that the equation \cos 2 x+a sin \;x=2 a-7 has a solution be [p, q] and r=\tan 9^{∘}-\tan 27^{∘}-\;{1}/{\cot 63^{∘}}+\tan 81^{∘}, then pqr is equal to [27-Jan-2024 Shift 1]

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