<prompt> Pointi P kwenye duara ya kipenyo cha 3 na inayozingatia asili ina uratibu wa duara left 3, frac3 pi8, fracpi5 kulia. Tafuta viwianishi vya duara vya nukta iliyo kinyume kipenyo cha P. Ingiza jibu lako katika fomu rho,theta,phi, ambapo rho 0, 0 le theta 2 pi, na 0 le phi le pi.  <response>: Pointi P imebainishwa na pembe theta na phi, kama inavyoonyeshwa hapa chini.asykuagiza tatu;ukubwa 180;makadirio ya sasa mtazamo 6,3,2;triple sphericaltorectangular rho halisi, theta halisi, phi halisi kurudi rhoSinphiCostheta,rhoSinphiSintheta,rhoCosphi;mara tatu O, P;O 0,0,0;P sphericaltorectangular 1,60,45;chora-1,0,0--1,0,0,Arrow36;chora0,-1,0--0,1,0,Arrow36;chora0,0,-1--0,0,1,Arrow36;kuchorausoO--P--P.x,P.y,0--cycle,kijivu0.7,nolight;kuchoraO--P--P.x,P.y,0--mzunguko;chora0,0,0.5..sphericaltorectangular0.5,60,452..sphericaltorectangular0.5,60,45,Arrow36;chora0.4,0,0..sphericaltorectangular0.4,30,90..sphericaltorectangular0.4,60,90,Arrow36;lebox, 1.1,0,0;leboy, 0,1.1,0;leboz, 0,0,1.1;lebophi, 0.2,0.25,0.6;lebotheta, 0.6,0.15,0;leboP, P, N;asyKwa nukta iliyo kinyume kiidadi ya P, theta theta pi na phi pi - phi.asykuagiza tatu;ukubwa 180;makadirio ya sasa mtazamo 6,3,2;triple sphericaltorectangular rho halisi, theta halisi, phi halisi kurudi rhoSinphiCostheta,rhoSinphiSintheta,rhoCosphi;mara tatu O, P, Q;O 0,0,0;P sphericaltorectangular 1,60,45;Q sphericaltorectangular 1,240,135;kuchorausoO--Q--Q.x,Q.y,0--cycle,kijivu0.7,nolight;chora-1,0,0--1,0,0,Arrow36;chora0,-1,0--0,1,0,Arrow36;chora0,0,-1--0,0,1,Arrow36;kuchoraO--P--P.x,P.y,0--mzunguko;kuchoraO--Q--Q.x,Q.y,0--mzunguko;chora0,0,0.5..sphericaltorectangular0.5,240,1352..sphericaltorectangular0.5,240,135,Arrow36;chora0.4,0,0..sphericaltorectangular0.4,120,90..sphericaltorectangular0.4,240,90,Arrow36;lebox, 1.1,0,0;leboy, 0,1.1,0;leboz, 0,0,1.1;lebophi, -0.2,-0.4,0.4;lebotheta, -0.6,0.25,0;leboP, P, N;asyKwa hivyo, viwianishi vya duara vya nukta iliyo kinyume kidiametrically P ni left 3, frac3 pi8 pi, pi - fracpi5 kulia kushoto 3, frac11 pi8, frac4 pi5 kulia. 