2 number cubes, which i'm assuming are dice, = 6^2, which = 36. The number of odd digits = 3, the number of even digits = 3. There are 18 odd totals and 18 even totals out of 36 outcomes, or 18/36, or 1/2.
If an angle it is obtuse it is between 90 and 180.
Angles in a quadrilateral add up to 360.
Therefore 3 obtuse angles must add up to AT LEAST 273 and if you then added the 90 it would get you to 363 which is too large so it cant be 90 :)

A standard approach would be the tangent half-angle substitution:

Then


from which we get

So the integral becomes

Rewrite the denominator as

and expand the integrand into its partial fractions:

We have



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