<s>[INST] Pythagorean Identities Simplify.
$\tan^2\frac{\pi}{3}-\cot(\frac{\pi}{4})+2\csc(\frac{\pi}{6})$
I am trying to help my little sister with homework and am rusty on my Pythagorean Identities. 
 [/INST] $$
\tan^2\frac{\pi}{3}-\cot(\frac{\pi}{4})+2\csc(\frac{\pi}{6})=\tan^2\frac{\pi}{3}-\frac{1}{\tan\frac{\pi}{4}}+2\frac{1}{\sin\frac{\pi}{6}}=\\ =\sqrt{3}^2-1+2\cdot 2=3-1+4=6
$$
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