Find 1/(sin 45 sin 46) + 1/(sin 47 sin 48) + ... + 1/(sin 133 sin 144).
\(=\frac{1}{ (sin 45 sin 46)} + \frac{1}{(sin 47 sin 48) }+ .. . + \frac{1}{sin (180-133) sin (180-144))}\\ =\frac{1}{ (sin 45 sin 46)} + \frac{1}{(sin 47 sin 48) }+ .. . + \frac{1}{sin (47) sin (46))}\\ =\frac{1}{ sin 45 sin 46} + \frac{1}{sin 46sin 47} + \frac{1}{sin 47 sin 48 }.....+ \frac{1}{sin89sin90}\\ \)
Yea, I know, that does not help much.