If  $A+B+C=\frac{\pi }{2}$  then ${\displaystyle \sum \frac{\cos \left(B+C\right)}{\cos B\cos C}=}$

${\displaystyle \sum \frac{\cos \left(B+C\right)}{\cos b\cos C}}$

$={\displaystyle \sum \frac{\cos B\cos C-\sin B\sin C}{\cos B\cos C}}$

$={\displaystyle \sum 1-\tan B\tan C}$

$=3-\left[\tan A\tan B+\tan B\tan C+\tan C\tan A\right]$

$=3-1=2$