# Functions here and there

**Geometry**Level 5

Solve for \(x\),

\[\sin\left[2\cos^{-1}\left\{\cot\left(2\tan^{-1}x\right)\right\}\right]=0\]

If \(x\) has \(n\) solutions, all of which can be represented in surd form, \[x_i = a_i+\sqrt{b_i}\]

\[\large \text{Evaluate }\left\{n + \sum\limits_{i=1}^n \left({\left|a_i\right| + \left|\sqrt{b_i}\right|}\right)\right\}\]