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According to the answer provided at the back of my textbook, the answer should be 4.70e6 N/C at 45 degrees.
I received the same answer of 4.7e6 N/C. Even when doing the calculations above I received 4.7e6 N/C
Solution manual has 4.7e6 as well.
Thanks for the heads up on this everyone. I forgot to square the denominator in the final calculation. I've updated the text answer, with a note about this error in the video for the final calculation.