Proof of $X+\csc{\left(\frac{\pi}{X}\right)}>2\csc{\left(\frac{\pi}{2X}\right)}$

Proof of
$X+\csc{\left(\frac{\pi}{X}\right)}>2\csc{\left(\frac{\pi}{2X}\right)}$

When $X$ is greater than 1, I want to prove that
$X+\csc{\left(\frac{\pi}{X}\right)}>2\csc{\left(\frac{\pi}{2X}\right)}$
where $\csc{(\cdot)}=\frac{1}{\sin{(\cdot)}}$.
Plotting the above expression using computer software, the plot shows the
inequality is true.
How to prove it mathematically?
Thanks in advance.