Answer
The solution on the interval $[0,2\pi )$, correct to four decimal places, is $1.9823$ or $4.3009$.
Work Step by Step
We have to calculate the equation using a calculator in radian mode:
$\theta ={{\cos }^{-1}}\frac{2}{5}\approx 1.1593$
And the cosine is negative in quadrants II and III,
$x\approx \pi -1.1593\ $
And the value of $\pi $ is 3.14159. Thus, the value of $x$ is:
$\begin{align}
& x\approx 3.14159-1.1593 \\
& \approx 1.9823
\end{align}$
or
$\ x\approx \pi +1.1593$
Thus, the value of $\pi $ is 3.14159. Thus, the value of $x$ is:
$\begin{align}
& x\approx 3.14159+1.1593 \\
& \approx 4.3009
\end{align}$
