let P=cos(2pi/7)+isin(2pi/7). the complex number a=P+P^2+P^4 is a root of the quadratic equation x^2+ax+b=0, where a and b are real.
1. prove 1+P+P^2+.....P^6=0
2. find the values of the coefficients a and b
3. deduce that -sin(pi/7)+sin(2pi/7)+sin(3pi/7)=root 7 times 0.5