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If $$f(x) = 2(\sin^6 x + \cos^6 x) - 3(\cos^4 x + \sin^4 x)$$, the value of $$f\left(\frac{\pi}{8}\right) - 3f\left(\frac{3\pi}{8}\right)$$ is
With $$s = \sin x$$ and $$c = \cos x$$, $$s^6 + c^6 = 1 - 3s^2c^2$$ and $$s^4 + c^4 = 1 - 2s^2c^2$$. So $$f(x) = 2 - 6s^2c^2 - 3 + 6s^2c^2 = -1$$ for every $$x$$. Hence $$f\left(\frac{\pi}{8}\right) - 3f\left(\frac{3\pi}{8}\right) = -1 + 3 = 2$$.
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