Question

[1 / (sin(45)sin(46))] + [1 / (sin(47)sin(48))] + ... + [1 / (sin(133)sin(134))] =?

Answer 1

Take it as a Series with first term as 45 and common difference as 2.
$a = a1 + (n-1)d$

Do the same for 46 through 144.
You will get a general Equation 1/sin(4n)sin(3n)(eg.)
Integrate it with 1 to Infinity. If the Answer is Finite, then Value is Finite or else it is infinite.