Correct answer is 39
\(\cos \mathrm{A}=\frac{\mathrm{b}^{2}+\mathrm{c}^{2}-\mathrm{a}^{2}}{2 \mathrm{bc}}\)
\(\frac{2}{3}=\frac{8^{2}+\mathrm{c}^{2}-7^{2}}{2 \times 8 \times \mathrm{c}}\)
C = 9
\(\cos \mathrm{C}=\frac{7^{2}+8^{2}-9^{2}}{2 \times 7 \times 8}=\frac{2}{7}\)
\(49 \cos 3 \mathrm{C}+42\)
\(49\left(4 \cos ^{3} \mathrm{C}-3 \cos \mathrm{C}\right)+42\)
\(49\left(4\left(\frac{2}{7}\right)^{3}-3\left(\frac{2}{7}\right)\right)+42\)
\(=\frac{32}{7}\)
\(\mathrm{m}+\mathrm{n}=32+7=39\)
