Find the real zeros of the trigonometric function on the interval $0 \leq θ < 2 π$ .
$f (x) = - \sin (2 x) + \sin x$

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$Final Answer: The real zeros of the function - \sin (2 x) + \sin (x) on the interval 0 \leq x < 2 π are 0, 1.04719755119660, 3.14159265358979, and 5.23598775598299$

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Step 1 ：We are given the function $f (x) = - \sin (2 x) + \sin (x)$ and we need to find the real zeros of this function in the interval $0 \leq x < 2 π$ .

Step 2 ：The real zeros of a function are the x-values for which the function equals zero. So, we need to solve the equation $- \sin (2 x) + \sin (x) = 0$ for $x$ in the interval $0 \leq x < 2 π$ .

Step 3 ：Solving the equation gives us the values $x = 0$ , $x = 1.04719755119660$ , $x = 3.14159265358979$ , and $x = 5.23598775598299$ .

Step 4 ： $Final Answer: The real zeros of the function - \sin (2 x) + \sin (x) on the interval 0 \leq x < 2 π are 0, 1.04719755119660, 3.14159265358979, and 5.23598775598299$

Find the real zeros of the trigonometric function on the interval 0≤θ<2π.f(x)=−sin⁡(2x)+sin⁡x

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Find the real zeros of the trigonometric function on the interval $0 \leq θ < 2 π$ .
$f (x) = - \sin (2 x) + \sin x$