\(476-\left\{5\cdot\left[409-\left(8\cdot3-21\right)^2\right]-17\cdot24\right\}\)
\(=476-\left\{5\cdot\left[409-3^2\right]-408\right\}\)
\(=476-\left\{5\cdot\left[409-9\right]-408\right\}\)
\(=476-\left\{5\cdot400-408\right\}\)
\(=476-\left\{2000-408\right\}\)
\(=476-1592\)
\(=-1116\)