If $2 \sin\theta+3 \cos\theta=2$ and $\theta \neq (2n+1)\frac{\pi}{2}$ then $\sin\theta+\cos\theta=$
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Equations of the form $a\sin\theta + b\cos\theta = c$ can be solved effectively using the tangent half-angle substitutions: $\sin\theta = \frac{2t}{1+t^2}$ and $\cos\theta = \frac{1-t^2}{1+t^2}$ where $t = \tan(\theta/2)$. This transforms the trigonometric equation into a quadratic equation in $t$.