Can the Solutions be found out

Let N be the no. of solutions of the equation given in the interval of $\left[ 0,2\pi \right]$

$\frac { 5 }{ 4 } \cos ^{ 2 }{ 2x } +\cos ^{ 4 }{ x } +\sin ^{ 4 }{ x } +\cos ^{ 6 }{ x } +\sin ^{ 6 }{ x }$ = 2

Let the solutions be represented by ${ \alpha }_{ 1 }{ ,\alpha }_{ 2 }{ ,\alpha }_{ 3 }{ ,\alpha }_{ 4 },......{ \alpha }_{ N }$ then value of P where P = $\prod _{ i=1 }^{ N }{ { \alpha }_{ i } }$ is represented by $\frac { { A }{ \pi }^{ B } }{ C }$ then value of A+B+C is