Problem $2.$ Image Rotation

$(10$ points$)$

Consider the barbara.png image. Convert it to Grayscale using library function. Write a function to perform image rotation by an arbitrary angle. Display the output rotated image for $\backslash (30^\{\backslash$circ$\},45^\{\backslash$circ$\},60^\{\backslash$circ$\}\backslash )$ and $\backslash (90^\{\backslash$circ$\}\backslash )$ degree $($CCW$)$ rotation w$.$r$.$t vertical, with nearest neighbour and bilinear interpolation. You're not allowed to use library functions for Image Rotation.