$\int_{0}^{\pi/2} \frac{\arctan^2 \left ( \sin^2 x \right )}{\sin^2 x} \, {\rm d}x$ [duplicate]

Does anyone have any ideas on how to attack this:

$$\int_{0}^{\pi/2} \frac{\arctan^2 \left ( \sin^2 x \right )}{\sin^2 x} \, {\rm d}x$$

I cannot think of something that could work. Wolfram Alpha does not evaluate it either.

• What makes you think there even is a solution in elementary functions? – Alfred Yerger Sep 10 '16 at 19:20
• This integral was proposed by M.L.Glasser so I guess it has. I don't know where it was proposed though neither do I know any other details. – Tolaso Sep 10 '16 at 19:21
• math.stackexchange.com/questions/1741089/… – nospoon Sep 10 '16 at 19:48
• No way I would have derived that answer!.. Way beyond my league! Thanks @nospoon – Tolaso Sep 10 '16 at 19:52
• @Tolaso Sure. You do ask very interesting questions, so keep it up. – nospoon Sep 10 '16 at 19:54