The answer is indefinite, since both tangent and sin are cyclic functions.
If we look for the largest angle between 0 and 2π, then we set
sin(x)-tan(x) = 0.005 (for two significant digits)
Solving for x, we get
Check: sin(x) = -0.2129628
tan(x) = -0.2179628
Thus sin(x) and tan(x) agree within 2 significant figures.
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