Answer
$$\theta=69.6^\circ$$
Work Step by Step
$$\cos\theta=\sin\Big(\frac{\theta}{4}+3^\circ\Big)\hspace{1cm}(1)$$
We already get from the cofunction identity that
$$\cos\theta=\sin(90^\circ-\theta)$$
That means using that in $(1)$, it can lead to
$$\sin(90^\circ-\theta)=\sin\Big(\frac{\theta}{4}+3^\circ\Big)$$
$$90^\circ-\theta=\frac{\theta}{4}+3^\circ$$
$$\frac{5\theta}{4}=87^\circ$$
$$\theta=\frac{87^\circ}{\frac{5}{4}}=\frac{87^\circ\times4}{5}$$
$$\theta=69.6^\circ$$
