summation - How to evaluate $sum_{n=1}^m 2^n arctan 2^n theta$

I need to evaluate

$$\sum_{n=1}^m 2^n \arctan 2^n \theta$$ as a function of $m$ and $\theta$. All I've done so far is write out the series explicitly:

$$\sum_{n=1}^m 2^n \arctan 2^n \theta = 2 \arctan 2\theta + 4\arctan 4\theta + 8\arctan 8\theta + \cdots + 2^m \arctan 2^m \theta$$

and I initially considered pairing every two terms up to use the $\arctan x + \arctan y$ trick, but it doesn't work because each $\arctan$ term has a different coefficient.