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\(3tan^2 45^{\circ}-sin^2 60^{\circ} - \cfrac{1}{3} cos^2 30^{\circ}-\cfrac{1}{8}sec^2 45^{\circ}\)
\(=3\times(1)^2-(\cfrac{\sqrt3}{2})^2 - \cfrac{1}{3} (\cfrac{\sqrt3}{2})^2 -\cfrac{1}{8} (\sqrt2)^2\)
\(=3-\cfrac{3}{4}-\cfrac{1}{\cancel3}\times \cfrac{\cancel3}{4}-\cfrac{1}{\cancel84} \times \cancel2\)
\(=3-\cfrac{3}{4}-\cfrac{1}{4}-\cfrac{1}{4}\)
\(=\cfrac{12-3-1-1}{4}\)
\(=\cfrac{7}{4}\) [Answer]