costheta+sintheta=cos2theta+sin2theta.
:. ul(cos2theta-costheta)+ul(sin2theta-sintheta)=0.
:. -2sin(3/2theta)sin(1/2theta)+2cos(3/2theta)sin(1/2theta)=0.
:. 2sin(1/2theta){cos(3/2theta)-sin(3/2theta)}=0.
:. sin(1/2theta)=0, or, sin(3/2theta)=cos(3/2theta).
"If, "sin(1/2theta)=0," then, "1/2theta=kpi, k in ZZ,
or, theta=2kpi, k in ZZ.
"In case, "sin(3/2theta)=cos(3/2theta)............(ast),
" then, "cos(3/2theta)!=0, because if "cos(3/2theta)=0,
" then "(ast) rArr sin(3/2theta)=0," and this contradicts "
sin^2(3/2theta)+cos^2(3/2theta)=0.
"So, dividing "(ast)" by "cos(3/2theta)," we get," tan(3/2theta)=1.
:. 3/2theta=kpi+pi/4, i.e., theta=2/3kpi+pi/6, k in ZZ.
Altogether, theta in {2kpi}uu{2/3kpi+pi/6}, k in ZZ.