If It's Stupid But It Works
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The other day, I got a request on Quora to calculate the sine of 18 degrees.
That sine is the cosine of 72 degrees, a fifth of 360 degrees, so it can be
calculated by a cubic equation because the cosine of twice 72 degrees is equal
to the cosine of thrice 72 degrees.
But, I used the cosine of 36 degrees, and the identity:
the cosine of 36 degrees is the negative of 4 times 36 degrees, so I found the
sign using a quartic (of degree 4) equation, so 0.5 was another zero of the
polynomial, and I found it using a method of finding a rational zero of a 
polynomial. Then having found the cosine of 36 degrees, I had to use a square 
root of a sum of a rational number and a radical.
Following is my solution:
https://archive.is/BQazB
It is not an upvoted one. Anyways,
if it's stupid but it works, it isn't stupid.