Prove $ \sqrt{\arctan(x)} = (1/2) \arccos((1-x)/(1+x))$ $$ \sqrt{\arctan(x)} = \dfrac{1}{2} \arccos\left(\dfrac{1-x}{1+x}\right)$$

I have been trying to solve this problem for the past hour, but I'm not able to solve it as I have just started solving difficult trigonometric problems. I'm not able to get any logic to solve this problem. I'm not able to put any trigonometric formula to solve this please help.
Here is 2-steps plan:


Salvage your accept rate from its current appalling value.
Prove that
$$ \arctan(\sqrt{x}) = \frac{1}{2} \arccos\left(\dfrac{1-x}{1+x}\right).
$$
Arctan . Jpeg

Click on that blue thingy above - and no, I swear this isn't a spam. The math formula programming was simply too tiring to learn in 3min. flat, so I've provided a written vers instead. Don't judge my handwriting, perhaps?
Hope it helped! :)