Let's practise the basics

Calculus Level 5

Find the minimum of

[(sin⁡t+2)2cos⁡2t+3cos⁡2t(sin⁡t+2)2]2.\left[ \frac{(\sin{t}+2)^2}{\cos^2t}+\frac{3\cos^2t}{(\sin{t}+2)^2} \right]^2.

From a calculus exam I recently gave.
Otto Bretscher by Otto Bretscher
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