finding an explicit formula from arctangent

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Seems straight-forward but i can't get it right;

I have this implicit equation: $$-2 \arctan{ \left( \frac{\sqrt{y-y^2}}{y} \right) } -x=c$$

where c is a constant.

I've to find the explicit equation for $y$... The solution given in the book is $y= \sin^2{\left(\frac{x}{2}+c'\right)}$

where $c'$ is a function of $c$. However my result is $y=\cos^2{\left(\frac{x}{2}+c'\right)}$ So..where's the mistake?

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just use $\sin(\theta + \pi/2)=\cos(\theta)$ and change slightly your $c'$ to get the same form as the book.