Limits, Continuity & Differentiability · Continuity of piecewise functions

Let

[t]

denote the greatest integer less than or equal to

t

. If the function

f(x) = \begin{cases} b^2\sin\left(\dfrac{\pi}{2}\left[\dfrac{\pi}{2}(\cos x + \sin x)\cos x\right]\right), & x < 0\\[10pt] \dfrac{\sin x - \frac12\sin 2x}{x^3}, & x > 0\\[10pt] a, & x = 0\end{cases}

is continuous at

x = 0

, then

a^2 + b^2

is equal to

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