Lagrangian function of pendulum

Homework Statement

Find the Lagrangian and the Lagrangian equations for this pendulum (see the picture). Radius of circle is a, mass of the bob is m and l is the length of the pendulum when it hangs straight down.

The Attempt at a Solution

I obtain:
$$L=\frac{1}{2}m(a^2\dot{\theta}^2+(l+a\theta)^2\dot{\theta}^2)-mg(a\sin\theta-(l+a\theta)\cos\theta)$$
while the answer in the book misses the term $$a^2\dot{\theta}^2$$ - where have I gone wrong?

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