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{\displaystyle {\begin{aligned}\sin {\frac {\pi }{32}}&={\tfrac {1}{2 ...

... {1}{2}}{\sqrt {2+{\sqrt {2-{\sqrt {2+{\sqrt {2}}}}}}}}&\quad \sin {\frac {7\pi }{16}}&={\tfrac {1}{2}}{\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}\\[6pt]\sin ...

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