The number of distinct real roots of the equation $P=\begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0$ in the interval $\bigg[ \large\frac{-\pi}{4} ,\frac{\pi}{4} \bigg]$ is :

Question

$\begin{array}{1 1} (1) 4 \\ (2) 3 \\ (3) 2 \\ (4) 1 \end{array}$