Let `alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/(15))` then `cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma` `tanalphatanbeta+tanbetatangamma+tanalphatangamma=1` `tanalpha+tanbeta+tangamma=tanalphatanbetatangamma` `cotalphacotbeta+cotbetacotgamma+cotalphacotgamma=1`

Explanation

`alpha=sin^(-1)(36/85),sinalpha=36/85,tanalpha=36/77`

`beta=cos^(-1)(4/5)=sinbeta=3/5,tanbeta=3/4`

`gamma=tan^(-1)(8/15),tangamma=8/15`

`tan(alpha+beta+gamma)=(sumtanalpha-pitanalpha)/(1-sumtanalphatanbeta)`

`=(36/77+3/9+8/15-36/77*3/4*8/15)/(1-(36/77*3/4+8/15*3/4+8/15*36/77))`

`tan(alpha+beta+gamma)=oo`

`alphaa+beta+gamma=pi/2`

`1=tanalphatanbeta+tanbetatangamma+tanalphatangamma`

...