I have $$ 34\csc\left(\dfrac{2\pi}{17}\right)$$ is equal to $$\dfrac{136}{\sqrt{8-\sqrt{15+\sqrt{17} + \sqrt{34 + 6\sqrt{17} - \sqrt{34-2\sqrt{17} } + 2\sqrt{ 578-34\sqrt{17}} - 16\sqrt{34-2\sqrt{17}} } }}}.$$
I want to rationalize it, but I am not sure where to start. Could anyone provide an explanation on how to rationalize this, and what should the answer be?
$$\csc^2\left(\frac{2\pi}{17}\right)=\frac{1}{17}\left[102+17\sqrt{17}-17\frac{\sqrt{34-2\sqrt{17}}}{2}-17\frac{\sqrt{34+2\sqrt{17}}}{2}+\sqrt{17}\cdot \sqrt{A}\right]$$ $$A=850+204\sqrt{17}-143{\sqrt{34+2\sqrt{17}}}-113{\sqrt{34-2\sqrt{17}}}$$ $$\tan^2\left(\dfrac{2\pi}{17}\right)=5+3\sqrt{17}+5\frac{\sqrt{34-2\sqrt{17}}}{2}+5\frac{\sqrt{34+2\sqrt{17}}}{2}-\sqrt{A}$$ $$A=850+204\sqrt{17}+161{\sqrt{34+2\sqrt{17}}}+127{\sqrt{34-2\sqrt{17}}}$$