Consider the cubic equation ${ x }^{ 3 }-\left( 1+\cos { \theta } +\sin { \theta } \right) { x }^{ 2 }+\left( \cos { \theta } \sin { \theta } +\cos { \theta } +\sin { \theta } \right) x-\sin { \theta } \cos { \theta } =0$ whose roots are ${ x }{ 1 },{ x }{ 2 },{ x }_{ 3 }$ The number of values of $\displaystyle \theta $ in $\displaystyle \left [ 0,2\pi \right ]$ for which at least two roots are equal
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