If 7x/12 is a double angle, 7x/24 is the (single) angle, and sin7x/12=2sin7x/24cos7x/24.
Example: if 7x/24=30 degrees or (pi)/6 then x=30*24/7=720/7 (about 102.86) degrees or (pi)/6*24/7=4(pi)/7 radians, and sin7x/12=sin1440/7 or sin8(pi)/7=2sin30cos30=(2)(1/2)(sqrt(3)/2)=sqrt(3)/2.