kill(all)$

fpprintprec:5$

van=facebook.com/LearningCalculus$

f(x):=tan(3*x/2)-2*sin(x)$
g(x):=2*sin(x)$

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

r:[newton(0.0000),newton(0.5236),newton(2.618),newton(3.6652),newton(5.7596),newton(6.2832)];

float(g(r));