A triangle CEF is drawn inside a square ABCD as shown in the figure. Given: CF = 8 cm, EF = 6 cm and CE = 10 cm. What is tan α + tan β equal to?

α is angle ECD (at C between CD and CE), β is angle FED (at E between EA and EF — actually β at E between EF and ED based on figure). Using the geometry of the triangle inside the square with derived side s = √(1296/13), and computing tan α = DE/DC component ratios and tan β = AF/AE-type ratios, the sum tan α + tan β = 17/16.