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Find the value of
cos475∘+sin475∘+3sin275∘cos275∘cos675∘+sin675∘+4sin275∘cos275∘.\frac{\cos^4 75^{\circ}+\sin^4 75^{\circ}+3\sin^2 75^{\circ}\cos^2 75^{\circ}}{\cos^6 75^{\circ}+\sin^6 75^{\circ}+4\sin^2 75^{\circ}\cos^2 75^{\circ}}.cos675∘+sin675∘+4sin275∘cos275∘cos475∘+sin475∘+3sin275∘cos275∘.
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