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find x,y,z

Source: 5-th Taiwanese Mathematical Olympiad 1996

January 11, 2007
trigonometrynumber theory proposednumber theory

Problem Statement

Suppose that a,b,ca,b,c are real numbers in (0,π2)(0,\frac{\pi}{2}) such that a+b+c=π4a+b+c=\frac{\pi}{4} and tan⁡a=1x,tan⁡b=1y,tan⁡c=1z\tan{a}=\frac{1}{x},\tan{b}=\frac{1}{y},\tan{c}=\frac{1}{z} , where x,y,zx,y,z are positive integer numbers. Find x,y,zx,y,z.
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