How to find bond energy of c-c bond in ethane from data

Balancing the equation :

2C + 3H2 → C2H6 ..............ΔH(1)= -84.67 kJ/mol

2C(graphite) → 2C(g) ........ ΔH(2)= 716.7 x 2 kJ/mol 

3H2→ 6H (g).......................ΔH(3)=435.9 x 3 kJ/mol

Adding the above equations and their enthalpies :

C2H6 → 2C(g) + 6H(g) ΔH(4)= 2828.4 kJ/mol

ΔH(4) = ΔH (C-C) +ΔH ( C-H)

ΔH (C-C) = ΔH(4) - ΔH ( C-H)

ΔH (C-C) = [2828.4-6 X 414.22] = 343.08 KJ/mol