$$3T+2-\frac{2t+3}{3}=\frac{4\pi}{3}$$
$T=\frac{2t}{9}+\frac{4\pi }{9}-\frac{1}{3}$
$$9T+6-\left(2t+3\right)=4\pi $$
$$9T+6-2t-3=4\pi $$
$$9T+3-2t=4\pi $$
$$9T-2t=4\pi -3$$
$$9T=4\pi -3+2t$$
$$9T=2t+4\pi -3$$
$$\frac{9T}{9}=\frac{2t+4\pi -3}{9}$$
$$T=\frac{2t+4\pi -3}{9}$$
$$T=\frac{2t}{9}+\frac{4\pi }{9}-\frac{1}{3}$$
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$t=\frac{9T}{2}+\frac{3}{2}-2\pi $
$$3-2t=4\pi -9T$$
$$-2t=4\pi -9T-3$$
$$-2t=-9T+4\pi -3$$
$$\frac{-2t}{-2}=\frac{-9T+4\pi -3}{-2}$$
$$t=\frac{-9T+4\pi -3}{-2}$$
$$t=\frac{9T}{2}+\frac{3}{2}-2\pi $$
