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If $\sin\theta - \cos\theta = 0$, then find the value of $\sin^4\theta + \cos^4\theta$.
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$$\begin{aligned}& \sin\theta - \cos\theta = 0 \Rightarrow \sin\theta = \cos\theta \Rightarrow \tan\theta = 1 \\ & Rightarrow \theta = 45^\circ \\ & sin^4 45^\circ + \cos^4 45^\circ = (\frac{1}{\sqrt{2}})^4 + (\frac{1}{\sqrt{2}})^4 \\ & = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\end{aligned}$$