Matrices 1

Calculus Level 2

Let $0<a<b<\frac { \pi }{ 2 }$ . If $f\left( x \right) =\left| \begin{matrix} \sin { x } & \sin { a } & \sin { b } \\ \cos { x } & \cos { a } & \cos { b } \\ \tan { x } & \tan { a } & \tan { b } \end{matrix} \right|$ , then minimum possible number of roots of $f'\left( x \right) =0$ lying in $(a,b)$ is: