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Evaluate the following expression.
$$\frac{\tan^2 60^\circ + \cosec^2 30^\circ \sin 90^\circ + 3\sec^2 30^\circ}{4\sin^2 45^\circ + \sec^2 60^\circ - \cot^2 30^\circ - 5\cos^2 90^\circ}$$
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