As θ runs over all real values, the expression 4·sinθ·cosθ takes exactly the values:

4·sinθ·cosθ = 2·(2sinθ·cosθ) = 2sin2θ, and sin2θ sweeps the whole interval −1 to 1, so the expression sweeps −2 to 2. Multiplying the individual bounds of sinθ and cosθ suggests the wrong −4 to 4.