<prompt> Pata thamani ya juu zaidi yaanzavmatrix 1 1 1 1 1 sin theta 1 1 cos theta 1 1 endvmatrix,kama masafa ya theta juu ya pembe zote.  <response>: Tunaweza kupanua kibainishi kama ifuatavyo:anzaalignanzavmatrix 1 1 1 1 1 dhambi theta 1 1 cos theta 1 1 mwishovmatrix anzavmatrix 1 dhambi theta 1 1 1 mwishovmatrix - anzavmatrix 1 1 1 cos theta 1 mwishovmatrix anzavmatrix 1 1 dhambi theta 1 cos theta 1 mwishovmatrix 1 dhambi theta - 1 - 1 - 1 cos theta 1 - 1 dhambi theta1 cos theta -cos theta sin theta -frac2 cos theta sin theta2 -fracsin 2 theta2.endalignThamani ya juu zaidi ya kibainishi basi ni frac12. 