Trigonometry - compound angles

ai) Show that csc C = cot (C/2) - cot C
ii) Using i, deduce the values of cot 3.14/8 and cot 5*3.14/12 in surd form
b) using a, express cscC + csc2C + csc4C + csc8C as the difference of two
contangents.
hence,prove that, without using tables or calculator, that
scs 2*3.14/5 + csc 4*3.14/5 +csc 8*3.14/5 + csc16*3.14/5 = 0


要由左 prove 到右 OR 右prove 到左
用慢d ge方法,多step