kill(all)$

ratprint:false$

van=facebook.com/LearningCalculus$

red(x):=tan(x)-tan(2*x)*tan(3*x)*tan(4*x)$

trigrat(red(x));

solve(%,x);

green(x):=sin(7*x) - sin(5*x) - sin(x);

newton(t):=float(subst(t,x,x-green(x)/diff(green(x),x)))$

root1: 0; green(root1)$
root2: newton(newton(newton(0.17453293)));
root3: newton(newton(newton(0.87266463)));
root4: newton(newton(newton(1.2217305)));
root5: newton(newton(newton(1.9198622)));
root6: newton(newton(newton(2.268928)));
root7: newton(newton(newton(2.9670597)));
root8: %pi; green(root8)$