Question 1185531
{{{(e^(i*theta))^3 = e^(3*i*theta)}}}


===> {{{(cos(theta)+i*sin(theta))^3 = cos(3*theta)+i*sin(3*theta)}}}

===> {{{cos^3(theta) +3*cos^2(theta)*i*sin(theta) + 3*cos(theta)*i^2*sin^2(theta)+i^3*sin^3(theta)  =  cos(3*theta)+i*sin(3*theta)}}}

===> {{{cos^3(theta) +3*cos^2(theta)*i*sin(theta) - 3*cos(theta)*sin^2(theta)-i*sin^3(theta)  =  cos(3*theta)+i*sin(3*theta)}}}

===> {{{(cos^3(theta)- 3*cos(theta)*sin^2(theta)) +i*(3*cos^2(theta)*sin(theta) -sin^3(theta))  =  cos(3*theta)+i*sin(3*theta)}}}


Equate the respective real and imaginary parts from the two sides and you'll get the answer.