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Find the minimum of
[(sint+2)2cos2t+3cos2t(sint+2)2]2.\left[ \frac{(\sin{t}+2)^2}{\cos^2t}+\frac{3\cos^2t}{(\sin{t}+2)^2} \right]^2.[cos2t(sint+2)2+(sint+2)23cos2t]2.
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