Hi Alan...great job thanks!
Prior to posting question and after long hours of problem solving I did obtain 36 deg and 108 degrees. My main issue was applying the standard formulas for the general angle...in this case cosine. Therefore I am now trying to see how I can reconcile those answers....hopefully I can solve !
All the best for Xmas of course and New Year....thanks again!
I did not really understand exactly second part of question but I have interpreted it as follows:
Define Pattern :
Sc = 13 + 33 + 53..........+ (2n-1)3 = n2(2n2-1) (as per formula for sum of cubes for odd integers)
Now Sum of cubes for n+(n+1)
S2n+1 = n2(2n2-1) + [ 2(n+1)-1]3
= 2n4- n2 + [2n+1]3
= 2n4- n2 + 8n3+ 12n2 + 6n + 1
= (2n4 + 4n3 + 2n2) + (4n3 + 8n2 + 4n) + (n2 + 2n + 1)
= 2n2(n+1)2 + 4n(n+1)2 + (n+1)2
= (n+1)2(2n2 + 4n + 1)