The above shows twos functions on a same Cartesian Plane: \( f(x) \) and \(f^\theta (x) \) colored blue and red respectively.

Let \(f(x)=x^3-6x^2+6x+1\)

Define \(f^{\theta}(x)\), where \(\theta \geq 0\), as the new graph obtained by rotating the graph of \(f(x)\) \(\theta\) degrees about the origin (\(0,0\)) in the **clockwise** direction.

Find the maximum value of \(\theta_M\) such that for all values of \(0<\theta<\theta_M\), \(f^{\theta}(x)\) has every value of \(x\) paired with only one \(y\) (more simply, no two points can have the same \(x\)-coordinate).

Input your answer as \(\lfloor 100\cdot\theta_m \rfloor \). Where \(\lfloor x \rfloor\) is the floor function which means the greatest integer less than or equal to \(x\).

This is part of the set Trevor's Ten

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