Number of solutions of the equation 4sin2x+tan2x+cot2x+cosec2x=6 in 0,π is

We have 4sin2x+tan2x+cot2x+cosec2x=64sin2xcos2x1cos2x+tan2x+cot2x+1+cot2x=64tan2xsec2x+tan2x+2cot2x=5Let  tanx=t⇒4t21+t2+t2+2t2=54t4+t4(1+t2)+2(1+t2)t2(1+t2)=54t4+t4+t6+2+2t2=5t2+5t4⇒t6−3t2+2=0 clearly +1,-1 are roots using sythetic division⇒t2−1t4+t2−2=0⇒t2=1,t2=−2(not possible) ⇒t2=1⇒t=±1 ⇒tanx=±1  ⇒x=π4,3π4