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arccos(1/2+cos(pi*(-x^2+2*x+2)/(x^2+4*x+7)))=(2*Pi)/3 equation

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Numerical solution:

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The solution

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    /       /   /   2          \\\       
    |1      |pi*\- x  + 2*x + 2/||   2*pi
acos|- + cos|-------------------|| = ----
    |2      |     2             ||    3  
    \       \    x  + 4*x + 7   //       
$$\operatorname{acos}{\left(\cos{\left(\frac{\pi \left(\left(- x^{2} + 2 x\right) + 2\right)}{\left(x^{2} + 4 x\right) + 7} \right)} + \frac{1}{2} \right)} = \frac{2 \pi}{3}$$
The graph
Numerical answer [src]
x1 = -0.5 - 1.5*i
x2 = -0.5 + 1.5*i
x3 = -0.5 + 1.5*i
x4 = -0.5 - 1.5*i
x4 = -0.5 - 1.5*i