128 pie-shaped sectors

Suppose you have two disks each with 128 pie-shaped sectors. one disk has 32 red sectors and 96 white sectors. the other disk has 64 white sectors and 64 red sectors. the two patterns can be completely arbitrary. can we place one over the other such that at least 64 sectors on each disk have the same color? Is this similar to letters and envelopes? I am not sure about the approach and answer. Can someone help?

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$