Hint to prove that $-\frac{1}{x^2}+\frac{1}{\sin^2(x)}$ is a convex function in the interval $[0 ,\pi/2]$

Question

Can you give me a hint on proving the function $f(x)=-\frac{1}{x^2}+\frac{1}{\sin^2(x)}$ is a convex function in the interval $[0 , \pi/2]$?

I am familiar with Jensen's inequality and second order derivative, but I couldn't apply them here.