<prompt> Ikiwa 0 theta fracpi2 na sqrt3 cos theta - sin theta frac13, basi tafuta sqrt3 dhambi theta cos theta.  <response>: Kutoka sqrt3 cos theta - sin theta frac13,sin theta sqrt3 cos theta - frac13.Kubadilisha hadi sin2 theta cos2 theta 1, tunapata3 cos2 theta - frac2 sqrt33 cos theta frac19 cos2 theta 1.Hii hurahisisha hadi 18 cos2 theta - 3 sqrt3 cos theta - 4 0. Kwa fomula ya quadratic,cos theta fracsqrt3 pm sqrt3512.Tangu 0 theta fracpi2, cos theta ni chanya, kwa hivyo cos theta fracsqrt3 sqrt3512.Kwa hivyo,anzaalignsqrt3 sin theta cos theta sqrt3 kushoto sqrt3 cos theta - frac13 kulia cos theta 3 cos theta - fracsqrt33 cos theta 4 cos theta - fracsqrt33 fracsqrt3 sqrt353 - fracsqrt33 fracsqrt353.mwishopanga 