Intersecting lines

Geometry Level 3

If (a,b)(a,b) is a point of intersection of the lines xcosθ+ysinθ=3x\cos\theta+y\sin\theta=3 and xsinθycosθ=4x\sin\theta -y\cos\theta=4, where θ\theta is a parameter, then find the maximum value of 2W2^W where W=(a+b2)W = {\left( \dfrac{a+b}{\sqrt{2}} \right) }.

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