Answer
The solution on the interval $[0,2\pi )$, correct to four decimal places, is $2.1790$ or $4.1041$.
Work Step by Step
We have to calculate the equation using a calculator in radian mode:
$\theta ={{\cos }^{-1}}\frac{4}{7}\approx 0.9626$
And the cosine is negative in quadrants II and III,
$x\approx \pi -0.9626$
And the value of $\pi $ is 3.14159. Thus, the value of $x$ is:
$\begin{align}
& x\approx 3.14159-0.9626 \\
& \approx 2.1790
\end{align}$
or
$x\approx \pi +0.9626$
And the value of $\pi $ is 3.14159.
Hence, the value of $x$ is:
$\begin{align}
& x\approx 3.14159+0.9626 \\
& \approx 4.1041
\end{align}$
