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i was just practicing my trigonometry. And i always find finding value of trigonometric inverse functions without a calculator to be hard. Can you guys give me questions to work with? For example, finding $\theta$ such that $$\theta = \arctan(2-\sqrt3)$$
Thanks in advance. Don't go easy on me :)

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    $\begingroup$ Find $\arctan1+\arctan2+\arctan3$. $\endgroup$ – Ivan Neretin Nov 3 '15 at 13:32
  • $\begingroup$ It is hard,and it almost not meant to be done by hand,almost never. $\endgroup$ – TheCoolDrop Nov 3 '15 at 13:32
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To name just a few..

  • Evaluate $\sin(\arctan(4))$
  • Find the inverse of $1 + 2\cos\left(\frac{\pi}{3(t+1)}\right)$
  • Prove $\arctan(a) + \arctan(b) = \begin{cases} \arctan \left(\frac{a+b}{1-ab}\right), & ab < 1 \\ \arctan \left(\frac{a+b}{1-ab}\right) + \pi, & ab > 1, a,b > 0 \\ \arctan \left(\frac{a+b}{1-ab}\right) - \pi, & ab > 1, a,b < 0 \end{cases}$
  • Find $\sum_{n=1}^{m}\arctan\left({\frac{1}{{n^2+n+1}}}\right)$

More to be added, stay tuned!

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