Trigonometry · Maximum and minimum of trigonometric expressions

Let

\alpha

and

\beta

respectively be the maximum and the minimum values of the function

f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right),\quad \theta \in \mathbb{R}.

Then

\alpha + 2\beta

is equal to:

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