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Verified answer
Sin A - sin B = 2 cos ¹/₂ (A+B) sin ¹/₂ (A - B)..
sin (4θ+α) - sin (4θ- α) = 2 cos ¹/₂ {4θ+α+4θ-α) sin¹/₂ (4θ+α -4θ+α)
= 2 cos 4θ sin α