<s>[INST] How to see if this functions are linearly independent? 
Is this set linearly independent? $A=\left\{ \arctan(x), \arctan(2x), \arctan\big(\frac{3x}{1-2x^2}\big)\right\}$

I've tried using the Wronskian
$$W(A)= \left| \begin{array}{ccc}
\arctan(x) & \arctan(2x) & \arctan\big(\frac{3x}{1-2x^2}\big) \\
\frac{1}{1+x^2} & \frac{2}{1+4x^2} & \frac{6x^2+3}{4x^2+5x^2+1} \\
-\frac{2x}{(x^2+1)^2} & -\frac{16x}{(4x^2+1)^2} & -\frac{6x(8x^4+8x^2+3)}{(4x^2+5x^2+1)^2} \end{array} \right|,$$
but expanding the determinant gives an extensive term difficult to simplify. So, does there exist an easier method to see whether the set is linearly independent?
 [/INST] Hint:
$$\arctan\frac{\tan a+\tan b}{1-\tan a\tan b}=a+b.$$
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