Solve {ccc}{1}&{cosθ}&{cos2θ}{cosθ}&{cos2θ}&{cos3θ}{cos2θ}&{cos3θ}&{cos4θ}

$$\left( \begin{array} { c c c } { 1 } & { \cos \theta } & { \cos 2 \theta } \\ { \cos \theta } & { \cos 2 \theta } & { \cos 3 \theta } \\ { \cos 2 \theta } & { \cos 3 \theta } & { \cos 4 \theta } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}1&\cos(\theta )&\cos(2\theta )\\\cos(\theta )&\cos(2\theta )&\cos(\theta )\left(\left(\cos(\theta )\right)^{2}-3\left(\sin(\theta )\right)^{2}\right)\\\cos(2\theta )&\cos(\theta )\left(\left(\cos(\theta )\right)^{2}-3\left(\sin(\theta )\right)^{2}\right)&\cos(4\theta )\end{matrix}\right)$$

Calculate Determinant

$$0$$