Solve[z+1+(1/z)==0]//N

(Sqrt[(((-0.5))^2)+(((0.866025))^2)])

ArcSin[0.866025]

ArcCos[-1/2]

Sin[th]

%//N

th=((2Pi)/3)
th//N
u[n_]:=C1*Cos[n*th]+C2*Sin[n*th]
u[n+1]+u[n]+u[n-1]==0//Simplify

Sin[1.0472]

Sin[th]

%//N

n=1
u[n+1]+u[n]+u[n-1]