Some (sum) cosines find tangent!!!

There's a typo in the first line. It should be $r$ instead of $i$

$\displaystyle \sum_{r=0}^{88}\frac {1}{(\cos(r))(\cos(r+1))}$

= $\displaystyle \sum_{r=0}^{88}\frac {\sin(1)}{(\cos(r))(\cos (r+1))\sin(1)}$

= $\displaystyle \sum_{r=0}^{88}\frac {\sin((r+1)-(r))}{(\cos(r))(\cos (r+1))\sin(1)}$

= $\displaystyle \sum_{r=0}^{88}\frac {\sin(r+1)\cos(r)-\cos(r+1)\sin(r))}{(\cos(r))(\cos (r+1))\sin(1)}$

= $\frac {1}{\sin (1)} \displaystyle \sum_{r=0}^{88}\tan(r+1)-\tan(r)$

= $\frac {\tan (89)-\tan (0)}{\sin (1)}$

$\Rightarrow \boxed{\theta =89}$