Rotating a Graph?

Calculus Level 5

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

Let f(x)=x36x2+6x+1f(x)=x^3-6x^2+6x+1

Define fθ(x)f^{\theta}(x), where θ0\theta \geq 0, as the new graph obtained by rotating the graph of f(x)f(x) θ\theta degrees about the origin (0,00,0) in the clockwise direction.

Find the maximum value of θM\theta_M such that for all values of 0<θ<θM0<\theta<\theta_M, fθ(x)f^{\theta}(x) has every value of xx paired with only one yy (more simply, no two points can have the same xx-coordinate).

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

This is part of the set Trevor's Ten


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