Factor polynomial x^7+1

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

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

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