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You can also try to play around with simplify_trig and simplify_radical:
sage: eq = (-2)^(1/3) == - 2^(1/3)
sage: bool(eq.simplify_radical())
True
sage: eq = cos(x)*(tan(x))^(1/3) == (sin(x)*(cos(x))^2)^(1/3)
sage: print eq.simplify_trig().simplify_radical()
sage: bool(eq.simplify_trig().simplify_radical())
True
