(Solved): Show that the function riv )=+sin2(3)8 has exactly one zero in the interval (,) ...

Show that the function riv $)=\theta +{\sin }^2\left(\frac{\theta }{3}\right)-8$ has exactly one zero in the interval $(-\infty ,\infty )$ Fole's Theorem statos that foc a function $f(x)$ that is continuous at every point over the dosed interval $(a,b)$ and diflerenfiatle at every point of its intenior $(a,b)$, If $(a)=4(b)$, then there is at least one number $\mathrm{c}$ in $(a,b)$ at which $\mathrm{f}(\mathrm{c})=0$. Find the derivative $\alpha (x)=\theta +{\sin }^2\left(\frac{\theta }{3}\right)-8$. $r(0)=$