(a * sin(pi/5)+b * cos(pi/5))/(a * cos(pi/5)-b * sin(pi/5))= sin(8 * pi/ 15)/cos(8 * pi/ 15)

(a * sin(pi/5)+b * cos(pi/5))* cos(8 * pi/ 15)=(a * cos(pi/5)-b * sin(pi/5))* sin(8 * pi/ 15)

Expand and merge similar projects.

a *(sin(8 * pi/ 15)* cos(pi/5)-sin(pi/5)* cos(8 * pi/ 15))= b *(cos(pi/5)* cos(8 * pi/ 15)+sin(pi/5)* sin(8 * pi/ 15))

Addition and subtraction formulas using sine and cosine

a * sin(8 * pi/ 15-pi/5)= b * cos(8 * pi/ 15-pi/5)

a * sin(π/3)= b * cos(π/3)

b/a = tan(π/3)=√3