Find the values of $\sin 2\alpha$, $\cos 2\alpha$ and $\tan 2\alpha$, when:
cosα=45\cos\alpha = \dfrac{4}{5}cosα=54, where 0<α<π20 < \alpha < \dfrac{\pi}{2}0<α<2π
Discuss theoretical concepts, mathematical formulas, and architectural foundations.
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