Trigonometry Problem?

Question

Can someone solve this for me. Thanks!
Find the least positive integer n such that 1/(sin 45 *sin 46) + 1/(sin 47 *sin 48) +...+1/(sin 133 *sin 134)=2/sin n. (all the angle measure is in degrees)

Answer 1

You have to sum up 45 terms which vary between 2 and 1. So the sum is going to be somewhere between 90 and 45. So sin n has to be between 1/45 and 1/22.5. But sin n is roughly n pi/ 180, so n/57.
n=2 is the only possible value.

Answer 2

By some calculation I have come to an answer of 4 degrees.
I know the exact exact answer may be close...!!!