The sum of all solutions in  0,4π of the equation tan+cotx+1=cosx+π4 is

We have tanx+cotx=cosx+π4−1tanx+cotx≤−2       and     cosx+π4−1≥−2It implies that equality holds when both are −2cosx+π4=−1⇒x+π4=(2n+1)π,n∈z⇒x=3π4 or  11π4⇒sum=7π2