I can't calculate the following integral

$$\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx=?$$

I can prove that it converges because:

$$\forall x\geq 0\quad \ln(x+1)\leq x$$

So : $$\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx<\int_{0}^{\infty} \frac{\sin^2(x)}{x^2}dx=\frac{\pi}{2}$$

Logically proceeding from my bound, I tried using power series without any success. See Wolfram alpha for more details. I think that integration by parts can give something interesting, but I cannot go further with that. I think it's not a hard integral but I cannot solve it.

Any help is greatly appreciated.

Thanks in advance for all your contributions.