Factor polynomial x+x^8/8

  /       3/7    /pi\      3/7    /pi\\ /     3/7    2/pi\    3/7    2/pi\\ /       3/7    2/pi\    3/7    2/pi\        3/7    /pi\    /pi\\ /       3/7    /pi\    /2*pi\    3/7    /pi\    /2*pi\      3/7    /pi\    /2*pi\      3/7    /2*pi\    /pi\\ /       3/7    /pi\    /2*pi\    3/7    /pi\    /2*pi\      3/7    /2*pi\    /pi\      3/7    /pi\    /2*pi\\ /     3/7    /pi\    /3*pi\    3/7    /pi\    /3*pi\      3/7    /pi\    /3*pi\      3/7    /3*pi\    /pi\\ /       3/7    /pi\    /3*pi\    3/7    /pi\    /3*pi\      3/7    /pi\    /3*pi\      3/7    /3*pi\    /pi\\
x*|x + - 2   *cos|--| - I*2   *sin|--||*|x + 2   *cos |--| + 2   *sin |--||*|x + - 2   *sin |--| + 2   *cos |--| + 2*I*2   *cos|--|*sin|--||*|x + - 2   *cos|--|*cos|----| + 2   *sin|--|*sin|----| - I*2   *cos|--|*sin|----| - I*2   *cos|----|*sin|--||*|x + - 2   *cos|--|*cos|----| - 2   *sin|--|*sin|----| - I*2   *cos|----|*sin|--| + I*2   *cos|--|*sin|----||*|x + 2   *cos|--|*cos|----| + 2   *sin|--|*sin|----| - I*2   *cos|--|*sin|----| + I*2   *cos|----|*sin|--||*|x + - 2   *sin|--|*sin|----| + 2   *cos|--|*cos|----| + I*2   *cos|--|*sin|----| + I*2   *cos|----|*sin|--||
  \              \7 /             \7 // \             \7 /            \7 // \               \7 /            \7 /               \7 /    \7 // \              \7 /    \ 7  /           \7 /    \ 7  /             \7 /    \ 7  /             \ 7  /    \7 // \              \7 /    \ 7  /           \7 /    \ 7  /             \ 7  /    \7 /             \7 /    \ 7  // \            \7 /    \ 7  /           \7 /    \ 7  /             \7 /    \ 7  /             \ 7  /    \7 // \              \7 /    \ 7  /           \7 /    \ 7  /             \7 /    \ 7  /             \ 7  /    \7 //

$$x \left(x + \left(- 2^{\frac{3}{7}} \cos{\left(\frac{\pi}{7} \right)} - 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(2^{\frac{3}{7}} \sin^{2}{\left(\frac{\pi}{7} \right)} + 2^{\frac{3}{7}} \cos^{2}{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- 2^{\frac{3}{7}} \sin^{2}{\left(\frac{\pi}{7} \right)} + 2^{\frac{3}{7}} \cos^{2}{\left(\frac{\pi}{7} \right)} + 2 \cdot 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- 2^{\frac{3}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + 2^{\frac{3}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - 2^{\frac{3}{7}} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} - 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(- 2^{\frac{3}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} - 2^{\frac{3}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + 2^{\frac{3}{7}} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(2^{\frac{3}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + 2^{\frac{3}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - 2^{\frac{3}{7}} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} + 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(x + \left(- 2^{\frac{3}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} + 2^{\frac{3}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + 2^{\frac{3}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + 2^{\frac{3}{7}} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right)$$

((((((x*(x - 2^(3/7)*cos(pi/7) - i*2^(3/7)*sin(pi/7)))*(x + 2^(3/7)*cos(pi/7)^2 + 2^(3/7)*sin(pi/7)^2))*(x - 2^(3/7)*sin(pi/7)^2 + 2^(3/7)*cos(pi/7)^2 + 2*i*2^(3/7)*cos(pi/7)*sin(pi/7)))*(x - 2^(3/7)*cos(pi/7)*cos(2*pi/7) + 2^(3/7)*sin(pi/7)*sin(2*pi/7) - i*2^(3/7)*cos(pi/7)*sin(2*pi/7) - i*2^(3/7)*cos(2*pi/7)*sin(pi/7)))*(x - 2^(3/7)*cos(pi/7)*cos(2*pi/7) - 2^(3/7)*sin(pi/7)*sin(2*pi/7) - i*2^(3/7)*cos(2*pi/7)*sin(pi/7) + i*2^(3/7)*cos(pi/7)*sin(2*pi/7)))*(x + 2^(3/7)*cos(pi/7)*cos(3*pi/7) + 2^(3/7)*sin(pi/7)*sin(3*pi/7) - i*2^(3/7)*cos(pi/7)*sin(3*pi/7) + i*2^(3/7)*cos(3*pi/7)*sin(pi/7)))*(x - 2^(3/7)*sin(pi/7)*sin(3*pi/7) + 2^(3/7)*cos(pi/7)*cos(3*pi/7) + i*2^(3/7)*cos(pi/7)*sin(3*pi/7) + i*2^(3/7)*cos(3*pi/7)*sin(pi/7))