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  4. Number of solutions of the equation | sin θ sin 2 θ sin 3 θ sin 2 θ sin 3 θ sin θ sin 3 θ sin θ sin 2 θ|=0 in [0,2 π] is

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Q. Number of solutions of the equation $\begin{vmatrix}\sin \theta & \sin 2 \theta & \sin 3 \theta \\ \sin 2 \theta & \sin 3 \theta & \sin \theta \\ \sin 3 \theta & \sin \theta & \sin 2 \theta\end{vmatrix}=0$ in $[0,2 \pi]$ is

Determinants

Solution:

We have, $(\sin \theta+\sin 2 \theta+\sin 3 \theta) \cdot\left[(\sin \theta-\sin 2 \theta)^2+(\sin 2 \theta-\sin 3 \theta)^2+(\sin 3 \theta-\sin \theta)^2\right]=0$

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