<prompt> Tafuta nambari kamili n kama hiyoarctanfrac 13 arctanfrac 14 arctanfrac 15 arctanfrac 1n frac pi4.  <response>: Kumbuka kuwa arctan frac13, arctan frac14, na arctan frac15 zote ni chini ya arctan frac 1sqrt3 fracpi6, kwa hivyo jumla yao ni kali.Kwa formula ya kuongeza tangent,tan arctan a arctan b fraca b1 - ab.Kishatan left arctan frac13 arctan frac14 kulia fracfrac13 frac1101 41 - frac13 cdot frac14 frac711,hivyoarctan frac13 arctan frac14 arctan frac711.Kishatan kushoto arctan frac13 arctan frac14 arctan frac15 kulia tan left arctan frac711 arctan frac15 kulia fracfrac711 frac151 - frac 711 cdot frac15 frac2324,hivyoarctan frac13 arctan frac14 arctan frac15 arctan frac2324.Kishaanzaalignfrac1n tan kushoto fracpi4 - arctan frac13 - arctan frac14 - arctan frac15 kulia tan kushoto fracpi4 - arctan frac2324 kulia frac1 - frac23241 frac 2324 frac147,mwishoalignhivyo n 47. 