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a)
f\left(x\right)=2\tan x-\sin2x
f\left(0\right)=2\tan0-\sin2\cdot0=2\cdot0-0=0
b)
f\left(\frac{\pi}{4}\right)=2\tan\frac{\pi}{4}-\sin\frac{\pi}{2}
2-1=1
c)
f\left(\frac{\pi}{6}\right)=2\tan\frac{\pi}{6}-\sin\frac{\pi}{3}
2\cdot\frac{1}{\sqrt{3}}-\frac{\sqrt{3}}{2}=\frac{2}{\sqrt{3}}-\frac{\sqrt{3}}{2}