Please help me with them problems:

1) if z^3=1, show that (1-z)(1-z^2)(1-z^4)(1-z^5)=9, zEC

2) if cos(x)+cos(y)+cos(t)=0, sin(x)+sin(y)+sin(t)=0 show that cos(3x)+cos(3y)+cos(3t)=3cos(x+y+t)

3)show that, the roots the equations (1+z)^(2n) +(1-z)^(2n)=0, nEN, zEC are given by the relation z=itan((2κ+1)π)/4n), κ=0,1,...,n-1

Thank you