<prompt> Kokotacos3 frac2 pi7 cos3 frac4 pi7 cos3 frac8 pi7.  <response>: Fomula ya pembe tatu inasema kuwa cos 3 theta 4 cos3 theta - 3 cos theta. Kishacos3 theta frac14 cos 3 theta frac34 cos theta.Kwa hiyo,anzaaligncos3 frac2 pi7 cos3 frac4 pi7 cos3 frac8 pi7 kushoto frac14 cos frac6 pi7 frac34 cos frac2 pi7 kulia kushoto frac 14 cos frac12 pi7 frac34 cos frac4 pi7 kulia kushoto frac1 4 cos frac24 pi7 frac34 cos frac8 pi7 kulia frac14 kushoto cos frac6 pi7 cos frac12 pi7 cos frac24 pi7 kulia frac34 kushoto cos frac2 pi7 cos frac4 pi7 cos frac8 pi 7 kulia frac14 kushoto cos frac6 pi7 cos frac2 pi7 cos frac4 pi7 kulia frac34 kushoto cos frac2 pi7 cos frac4 pi7 cos frac6 pi 7 kulia cos frac2 pi7 cos frac4 pi7 cos frac6 pi7.endalignFikiria jumlaS jina la operetacis 0 jina la operetacis frac2 pi7 jina la operetacis frac4 pi7 dots jina la operetacis frac12 pi7.KishaanzaalignS operatornamecis frac2 pi7 operatornamecis frac2 pi7 operatornamecis frac4 pi7 dots jina la operetacis frac12 pi7 jina la operetacis 2 pi jina la operetacis frac2 pi7 jina la operetacis frac4 pi7 vidoti jina la uendeshajicis frac12 pi 7 jina la operetacis 0 S,endalignhivyo S left 1 - jina la operetacis frac2 pi7 kulia 0. Kwa hivyo, S 0.Kuchukua sehemu halisi ya S kunatupacos 0 cos frac2 pi7 cos frac4 pi7 cos frac6 pi7 cos frac 8 pi7 cos frac10 pi7 cos frac12 pi7 0.Kisha1 cos frac2 pi7 cos frac4 pi7 cos frac6 pi7 cos frac6 pi7 cos frac4 pi7 cos frac2 pi7 0,hivyocos frac2 pi7 cos frac4 pi7 cos frac6 pi7 -frac12 . 