About client_manager mutex

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Hi~
I read the code of client_manager.go, and I have a question about mutex. For example:

one part:

func (m *ClientManager) Add(client *Client)

...
m.mu.Unlock()
m.removeOldest()
m.mu.Lock()

two part:

func (m *ClientManager) removeOldest() {
	m.mu.Lock()
	ele := m.ll.Back()
	m.mu.Unlock()
	if ele != nil {
		m.removeElement(ele)
	}
}

func (m *ClientManager) removeElement(e *list.Element) {
	m.mu.Lock()
	defer m.mu.Unlock()
	m.ll.Remove(e)
	delete(m.cache, e.Value.(*managerItem).key)
}

It seems that it can not need "two" m.mu.Lock ?

The below codes are right?
func (m *ClientManager) Add(client *Client)

...
m.removeOldest()

If I just use m.mu.Lock once, it is not good for high concurrency?

Can you answer me about this question?

I appreciate it