# Trig Power Challenge

Geometry Level 3

If the value of $\sin^{24}\frac{\pi}{24} + \cos^{24}\frac{\pi}{24}$

is expressed in simplest form as $$\dfrac{a + b\sqrt{c}}{d},$$ find the last three digits of $$a + b + c + d.$$

Note: Simplest form refers to the condition that $$a,b,c,d$$ are positive integers with $$\gcd(a,b,d)=1$$ and $$c$$ is not divisible by the square of any prime.

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