The number of values of θ  in the range 0≤θ≤360°  satisfying the equation cos42θ+2sin22θ=17(sinθ+cosθ)8  is

Given equation is (1-sin22θ)2+2sin22θ=17(1+sin2θ)4 Put x=sin2θ.  Therefore (1−x2)2+2x2=17(1+x)4x4+1=17(1+x)4=17(1+2x+x2)2 ]Clearly x=sin2θ=0  is not a solution of the given equation. Therefore dividing both sides of Eq.  by x2  we get x2+1x2=17(x+1x+2)2Putting x+1x=y,  we have y2−2=17(y+2)216y2+68y+70=0,  ⇒8y2+34y+35=0   ⇒(4y+7)(2y+5)=0From this we get    y=−74  or −52Case 1: If y=−7/4,  then 4x2+7x+4=0  has no real roots.Case 2: If y=−5/2,  then2x2+5x+2=0 ⇒x=-12, -2Now sin2θ=x=−2  is not possible . Therefore sin2θ=−1/2We get total 4 solutions