Writing a real valued expression in a form that does not include sqrt(-1)


I was wondering if the following real-valued expression (obtained with
a CAS) could be written in a form that does not include the imaginary
unit (denoted by i here). I would like to do this without using
trigonometric functions (actually this expression is equal to cos(pi/
9))

(1/2)*((1 + i*sqrt(3))/2)^(1/3) + (4*(1 + i*sqrt(3)))^(-1/3)

Is this possible?
.