If
\[
\int \frac{e^{\cos x}\sin x}{e^{\cos x}+e^{-\cos x}}\,dx
=
-\frac12\left[f(x)+\log\!\left(e^{\cos x}+e^{-\cos x}\right)\right]+c
\]
and
\[
f\!\left(\frac{\pi}{3}\right)=\frac12,
\]
then the number of points at which \(f(x)\) attains the maximum value in
\[
[-2\pi,2\pi]
\]
is